Ouch! That hurts!
The 'sad' answer is no, can't 'rebuild the database', but all may not be lost cause you say you have course backups.
First, create an archive (zip/tar) of the code directory and most importantly the 'filedir' inside the moodledata directory with what ever tool you have to do that. If you don't have such a tool, ask the provider to make a zip/tar of the code directory and the 'filedir' inside your moodledata for you AND provide access to those so you can down load them.
The tricky part here is how to extract the backups from the mess of stuff you'll find in 'filedir'. So the first questions for you: How did you backup the most important course? By using 'backup' in the course admin menu while in a course? If you had automated backups, did you leave the default location to Course backup filearea (that was the default)?
If you left the defaults, your backups are somewhere in moodledata/filedir/
Here's an example of where a backup file might be located in moodledata/filedir/:
./d4/1a/d41a96b0b1816f8472297df956086ce10486a675
The file, in /d4/1a/
now named 'd41a96b0b1816f8472297df956086ce10486a675' is a
Zip archive data, at least v2.0 to extract
That *might* be a backup of a course in Moodle (you could have uploaded zips in your course).
Is your provider willing to run a script inside the filedir so we can get clues like above?
for f in ./*/*/*; do echo "$f"; file -b "$f"; echo "-------"; done > listing.txt
Look through the listing.txt file ...
we are looking for things like this:
./62/53/6253293ad6fc7d651594771e5c24dc31b6cfa0c2
Zip archive data, at least v2.0 to extract
6253293ad6fc7d651594771e5c24dc31b6cfa0c2 *might* be a backup.
cp ./62/53/6253293ad6fc7d651594771e5c24dc31b6cfa0c2 /otherlocaation/maybebackup.zip
cd /otherlocation/
unzip -list maybebackup.zip (list the contents of a .zip)
With this last command, one will see what's in the zip.
If you see this - or something like it:
Length Date Time Name
-------- ---- ---- ----
0 11-26-13 14:36 activities/
0 11-26-13 14:36 activities/folder_1242/
137 11-26-13 14:36 activities/folder_1242/filters.xml
1093 11-26-13 14:36 activities/folder_1242/logs.xml
399 11-26-13 14:36 activities/folder_1242/folder.xml
151 11-26-13 14:36 activities/folder_1242/grades.xml
809 11-26-13 14:36 activities/folder_1242/module.xml
137 11-26-13 14:36 activities/folder_1242/roles.xml
61 11-26-13 14:36 activities/folder_1242/comments.xml
213 11-26-13 14:36 activities/folder_1242/inforef.xml
67 11-26-13 14:36 activities/folder_1242/completion.xml
57 11-26-13 14:36 activities/folder_1242/calendar.xml
0 11-26-13 14:36 activities/url_2802/
137 11-26-13 14:36 activities/url_2802/filters.xml
1094 11-26-13 14:36 activities/url_2802/logs.xml
554 11-26-13 14:36 activities/url_2802/url.xml
151 11-26-13 14:36 activities/url_2802/grades.xml
806 11-26-13 14:36 activities/url_2802/module.xml
137 11-26-13 14:36 activities/url_2802/roles.xml
61 11-26-13 14:36 activities/url_2802/comments.xml
59 11-26-13 14:36 activities/url_2802/inforef.xml
67 11-26-13 14:36 activities/url_2802/completion.xml
57 11-26-13 14:36 activities/url_2802/calendar.xml
0 11-26-13 14:36 activities/url_1239/
137 11-26-13 14:36 activities/url_1239/filters.xml
2128 11-26-13 14:36 activities/url_1239/logs.xml
525 11-26-13 14:36 activities/url_1239/url.xml
151 11-26-13 14:36 activities/url_1239/grades.xml
806 11-26-13 14:36 activities/url_1239/module.xml
137 11-26-13 14:36 activities/url_1239/roles.xml
61 11-26-13 14:36 activities/url_1239/comments.xml
59 11-26-13 14:36 activities/url_1239/inforef.xml
67 11-26-13 14:36 activities/url_1239/completion.xml
57 11-26-13 14:36 activities/url_1239/calendar.xml
0 11-26-13 14:36 activities/resource_1241/
137 11-26-13 14:36 activities/resource_1241/filters.xml
476 11-26-13 14:36 activities/resource_1241/logs.xml
598 11-26-13 14:36 activities/resource_1241/resource.xml
151 11-26-13 14:36 activities/resource_1241/grades.xml
811 11-26-13 14:36 activities/resource_1241/module.xml
137 11-26-13 14:36 activities/resource_1241/roles.xml
61 11-26-13 14:36 activities/resource_1241/comments.xml
170 11-26-13 14:36 activities/resource_1241/inforef.xml
67 11-26-13 14:36 activities/resource_1241/completion.xml
57 11-26-13 14:36 activities/resource_1241/calendar.xml
0 11-26-13 14:36 activities/resource_1240/
137 11-26-13 14:36 activities/resource_1240/filters.xml
688 11-26-13 14:36 activities/resource_1240/logs.xml
670 11-26-13 14:36 activities/resource_1240/resource.xml
151 11-26-13 14:36 activities/resource_1240/grades.xml
811 11-26-13 14:36 activities/resource_1240/module.xml
137 11-26-13 14:36 activities/resource_1240/roles.xml
61 11-26-13 14:36 activities/resource_1240/comments.xml
170 11-26-13 14:36 activities/resource_1240/inforef.xml
67 11-26-13 14:36 activities/resource_1240/completion.xml
57 11-26-13 14:36 activities/resource_1240/calendar.xml
57 11-26-13 14:36 badges.xml
79 11-26-13 14:36 completion.xml
0 11-26-13 14:36 course/
137 11-26-13 14:36 course/filters.xml
1139 11-26-13 14:36 course/course.xml
23807 11-26-13 14:36 course/logs.xml
0 11-26-13 14:36 course/blocks/
0 11-26-13 14:36 course/blocks/configurable_reports_109/
137 11-26-13 14:36 course/blocks/configurable_reports_109/roles.xml
61 11-26-13 14:36 course/blocks/configurable_reports_109/comments.xml
59 11-26-13 14:36 course/blocks/configurable_reports_109/inforef.xml
716 11-26-13 14:36 course/blocks/configurable_reports_109/block.xml
0 11-26-13 14:36 course/blocks/rss_client_153/
2451 11-26-13 14:36 course/blocks/rss_client_153/rss_client.xml
137 11-26-13 14:36 course/blocks/rss_client_153/roles.xml
61 11-26-13 14:36 course/blocks/rss_client_153/comments.xml
59 11-26-13 14:36 course/blocks/rss_client_153/inforef.xml
773 11-26-13 14:36 course/blocks/rss_client_153/block.xml
0 11-26-13 14:36 course/blocks/recent_activity_39/
137 11-26-13 14:36 course/blocks/recent_activity_39/roles.xml
61 11-26-13 14:36 course/blocks/recent_activity_39/comments.xml
59 11-26-13 14:36 course/blocks/recent_activity_39/inforef.xml
469 11-26-13 14:36 course/blocks/recent_activity_39/block.xml
4330 11-26-13 14:36 course/enrolments.xml
651 11-26-13 14:36 course/roles.xml
61 11-26-13 14:36 course/comments.xml
269 11-26-13 14:36 course/inforef.xml
57 11-26-13 14:36 course/calendar.xml
0 11-26-13 14:36 files/
0 11-26-13 14:36 files/eb/
23112 11-26-13 14:36 files/eb/eb18361160ca39c9044204416b7fb92203559302
0 11-26-13 14:36 files/8b/
8768 11-26-13 14:36 files/8b/8b4feb1b07b63a833124b24ec13d421c82a227ec
0 11-26-13 14:36 files/3b/
6994 11-26-13 14:36 files/3b/3b7607c22eba7346820c34321962607c39262e3d
0 11-26-13 14:36 files/d5/
323015 11-26-13 14:36 files/d5/d5260a8dee160145f3b2a079441cb6db785b5dc0
0 11-26-13 14:36 files/fe/
637767 11-26-13 14:36 files/fe/fe498d3442429a37fd79228236aaf256cb9f865a
0 11-26-13 14:36 files/77/
12947 11-26-13 14:36 files/77/77726b8c373455e2dc0844805d6e5f855e41ab24
0 11-26-13 14:36 files/d0/
3776 11-26-13 14:36 files/d0/d0e37bd48c19387ce2fae79d3726d8f85a915c9b
0 11-26-13 14:36 files/bd/
16051 11-26-13 14:36 files/bd/bd0e7ad0355a24c296886efd208242e2f53d43c3
0 11-26-13 14:36 files/25/
3195 11-26-13 14:36 files/25/253bea1bb72945010fdb456d2986c88d29a7796c
0 11-26-13 14:36 files/af/
2004 11-26-13 14:36 files/af/af5f3bd5e508843fb8176735896cf44b56ccb142
11026 11-26-13 14:36 files.xml
1790 11-26-13 14:36 gradebook.xml
86 11-26-13 14:36 groups.xml
7871 11-26-13 14:36 moodle_backup.xml
83 11-26-13 14:36 outcomes.xml
83 11-26-13 14:36 questions.xml
525 11-26-13 14:36 roles.xml
79 11-26-13 14:36 scales.xml
0 11-26-13 14:36 sections/
0 11-26-13 14:36 sections/section_536/
359 11-26-13 14:36 sections/section_536/section.xml
59 11-26-13 14:36 sections/section_536/inforef.xml
0 11-26-13 14:36 sections/section_568/
451 11-26-13 14:36 sections/section_568/section.xml
59 11-26-13 14:36 sections/section_568/inforef.xml
0 11-26-13 14:36 sections/section_537/
412 11-26-13 14:36 sections/section_537/section.xml
59 11-26-13 14:36 sections/section_537/inforef.xml
8834 11-26-13 14:36 users.xml
0 11-26-13 14:36 moodle_backup.log
-------- -------
1121161 125 files
*** IT'S A BACKUP COURSE! AND THAT ZIP FILE CAN BE RESTORE TO A MOODLE!!! ***
Now the next question ... what do you use as a workstation? Windows/Mac?
Hope it's a Mac, cause you could do what I've shown above on your Mac.
Now to get your site back on line ... *AFTER* backing up what you have and downloading ...
remove the config.php file from the code directory. You have a backup of it downloaded and can look at it locally.
Empty the moodledata directory. You have a backup of it downloaded. Jot down the path to the data directory cause you will be asked to provide the path.
Create a new blank database for your Moodle. You know the login/password to it.
Now, in a browser, hit your Moodle site and you should be in the install mode.
Once you have the site up and running, we can then concentrate on how to find and extract backups in the local 'filedir' zip/tar ball you downloaded - depends upon what platform you have locally.
*IF* we find them and then you can restore those to your Moodle.
Realize this might be a little much ... if it is, get this info to your provider ... above was done on a Linux server and they should be able to follow the above and get you some .zips. ;)
** That's the least they can do for you since they can't restore your DB!!! If they can't/won't do the above, I'd be thinking about where to host Moodle else where!
'spirit of sharing'. Ken