hmm im not sure what the issue is, hard to say when i cant get to the pc to have a look

i think from what you said the pcs that wont sign in are running the older version of I.E? if so make sure they have the latest, and also have you tried clearing temp files/history? even if you have download this and run it
http://www.filehippo.com/download_ccleaner/ (top right, click on download lastest version) basically this will do all the work for you, it will delete history and all that crap that sits on any pc until you delete it, excellent little program, just note that once you use this it will also delete saved passwords for websites so you will have to re-type everything.
After you have done all that, if it still doesnt work then try downloading a different web browser
http://www.filehippo.com/download_firefox/, thats firefox, ive been using this for the last year and its excellent, stops all the crappy pop ups etc, amongst other things that I.E cant do
If it STILL wont work, then im stumped