Can't connect to any game servers!

Does the computer have access to multiple networks or only your internet connection?
Also what type of connection is it?

It's Residential Internet, through Century Link 12 Mbps. This is my only internet connection besides tethering through my Verizon phone. But the internet shouldn't be the problem they work on other computers on the network.

Although I'm no expert on networking , it must be a case of bad ip address.
You will find much better help in this section - http://www.tomshardware.com/forum/forum-42.html
Select a best answer and close the thread.

even though I can connect to everything else fine?

Hmmm then I guess I was wrong.
Anyways as I mentioned before you will receive much better advice on the networking section regarding any connection issues. You can make a thread there and keep this thread open to get any advice you can.
Sorry but I'm only 15 and have very little experience in networking.
I always try my best to help though.
Good luck with your problem.

Will do, thanks for your help!

Maybe this can help (This won't change your router configurations , don't worry)
Not sure if this works on win 8 but it probably should.
1. Open the run command.
2. Type this exact same line in the run box - netsh int ip reset
3. Restart the computer.
4. Open run command again.
5. Type this exact same line - netsh winsock reset
6. Restart the computer again.
Now try connecting.
These are just some basic steps that I know but if this doesn't work then I really can't help you.
If you are wondering what they do then the first one resets the internet protocol (TCP/IP) and the second one resets your winsock entries.