Isnt there a way to plug your guitar into your computer to record it?
There's many ways. Do you want your amp tone, or will you use software?
amp tone amp tone!
I got an adapter from Radioshack and plugged it into my microphone jack, plus you'll need to get some recording software because the computers recorder won't get you anywhere.
amp>microfone(a decent one)>mic preamp>line in on pc or maybe even usb
All you really need is some good home recording software and a good audio interface.