I have just gone thru the same nightmare u are having with a ISP provider.
With me it turned out to be the internet provider and they moved me to another machine.
Here is a way to prove it, that worked for me.
First I downloaded a copy of Mozilla as it lets you view and remove the cookies easily, more easily than IE I found.
Now make a folder on your server in the folder that moodle is living in and call it test
Put into this folder this simple little script that I have attached, called php.test
Now using Mozilla with no cookies saved in it open up the script : ie www.icthelp.biz/moodle/test/test.php
You will see that the page opens and says:
The counter is now 0
- Counter initialized, please reload this page to see it increment
Now click refresh and the counter changes to:The counter is now 1
My problem was the server was killing the session in about 50 minnutes, yours may be different. What I did was to leave my mozilla open, not touching it for 60 minutes. I would come back hit refresh and found the session was being killed and had to be restarted in order for the script to continue. I even tried putting in a .htaccess file to override the session time(even though phpinfo showed session time as 4 hours), and it didnt work, it would still get killed in under 60 minutes.
I showed this to the techs at the ISP, they concurred there was a problem and they gave me a new server.