If you have a free network port on each PC all you will need is a crossover cable.
The OP said he bought a second NIC for his one computer and can't get it to work. Assuming the second computer needs access to the internet, the crossover cable is "all you will need" hardware wise (since he bought a second NIC), but not all he will need hassle wise.
He'll need to get the second NIC functioning properly, set up ICS in the home network setup wizard, and then always have his one PC powered on whenever he wants access to the internet from the other PC.
Taking the second NIC back and instead buying a router is much simpler, and gives each computer an independent connection to the internet, as well as providing the file sharing he was after.
Now, if he doesn't care about accessing the internet from the second computer, things are simpler, but he still needs to get his new NIC functioning.
While it should be easy I have to admit that windows built in ICS is not the best of solutions as Iceblue mentioned above. One thing that you could try is to use a 3rd party proxy server.
You can find a list of free ones here