Well, internet explorer sucks!!!!!NEVER use it. unless you got heavy pc protetion.
So reinstall firefox and is the problem is still there try modifying firewall settings, if you don't have one, then go to the internet explorer and try changing cookies settings.
If none of this works, go to mozilla adons and try some add-ons, download bars and such, that will change settings, one of them will eventually change it(this is a noob option).
Some time ago I could save GIF's but since I installed firefox, it's all ok.
BTW, some more details would be nice.
e.g. can you play java apps at browser?
what kind of files have you tried to download?