I've had Mandrake Linux and Redhat Linux on my computer before, but I was never able to setup a connection to the internet. Could this be because my computer's network card is incompatible with linux?

Network Card
• Integrated 10/100Base-T networking interface

That's taken from a site with my computers specific model's hardware. Would that mean that I'd have to buy a new motherboard, because it says it's integrated. It wouldn't be that big of a deal because my current motherboard STINKS.

I do have the money to buy a compatible network card, so if the problem is just my network card please point out a compatible network card for me.

My computers model is: Compaq Presario S5000CL , if that helps.

It may be incompatible but it is unlikely. What type of ethernet card are you using? There should be a chip number somewhere. Also try running:
dmesg | grep - eth
lspci

What output do you get?