Yes - I have an idea...
The laptops are all good - they all behave the same
The "modem" is fine because some pages load OK
The web sites you are going to - the ones that fail - are all bad. The ones where you fail at login time - you have wrong username/password combination.
You give few details so this is the best I can do - mind you even with more details I probably couldn't do better.
Good luck...
Peccavi, January 2010