So, if I understand correctly, your PC gets Wi-Fi from a USB adapter, and you want to share that connection with your 360. You didn't specify that you have a Wi-Fi adapter for your 360, so I'll assume you don't have one.
You say your PC doesn't have a NIC, and if it doesn't, your shit out of luck as far as I can tell. You'll have to get one, I'm sure they are super cheap on eBay or the like. Most motherboards have them built in if I am not mistaken though, so check to make sure.
Anyway, just connect the ethernet cable from your 360 to PC, and I am on Windows XP and just ran the Network and Setup Wizard. It will ask you how your PC connects to the internet, just choose the option that says 'other computers on my network will connect to the internet through this computer', then it will ask which connection provides Internet connectivity, which is where you would choose your wireless connection, and then it will ask which connection you want to share your internet with, and you'd choose 'Local Area Connection' or something similar. After I did all that, the XBox is connecting just fine, sucks I have to have my PC on all the time though.