Sorry about not getting back to you yesterday, Alex.
I probably should have mentioned this before, but the weird thing about this is that when I'm running XP on my computer (which has Vista Business installed), it occasionally disconnects. I'd say one every week, maybe even less than that. Once I'm back in Vista, however, I can't even go a full 6 hours without being disconnected. It's the same deal with Windows 7 too. Any insight on that?
I may have jumped the gun a bit in blaming your router; I assumed that when you lose the Internet, all of your devices lost it at the same time? Or is it only your computer? If it's only your computer, then it's not overly likely that it's your router's fault.
If you could still run those commands, it would be great; I'd like to know how severely you're losing your Internet connection. It may just be a poor signal, or a stagnant connection, etc. If possible, can you try connecting the computer directly to the modem via an Ethernet cable, and then see if you still lose your Internet connection? I know it will be hard, since it seems pretty random, but it could help to determine whether this is due to your router, or something else.
The best thing would be to try to find some warnings/errors in your Event Log/Viewer, since these errors may help provide some insight as to why you're losing your connection.
One final thing to try would be to run the computer in Safe Mode with Networking
to rule out software interference.