I am afraid the error codes you show are not meaningful to me, so I will stick witht he generic things to try first.
Connection usually fails for three reasons,
1. The password entered by the installer cannot access the database, it is incorrect, and is the most common reason actually. People swear it is not, but it is.
2. The database is not properly accessible via PHP because in Windows, PHP needs an additional set of instructions that are not always clear or readily available. Does the PHP run properly? Can you successfully run the phpinfo(); command? If you do, scroll all the way to the end, I did an install once not realising there was an error in the php.ini file. It took me a while to realise that some services were not being loaded, so I looked at the info file and as I scrolled down, it came to an abrupt end. It was almost installed, but when it got to the error, it stopped. Previously all I was doing was looking to make sure I had the first part.
3. Can you directly access the database server? I am not sure what charset the server uses, nor what charset Moodle requires in MSSQL, but check to make sure these are the same. Moodle may need a utf8_unicode_ci, whereas MSSQL might be using a Windows-1252 charset. I do not know, but I would check anyway. The basic is that the installed charset is different than the required utf8 unicode that is the second most common issue.
It would be extremely unlikely the database is "full", unless it is an organizational database, that is, one database for every operation, not one each, just one, and the hard drive the server uses is absolutely full. (The second more likely than the first, but if the system has no drive use alert, then I suggest someone is not doing their job, yet another unlikely scenario in this IT sensitive age.)