After I burned out a soundcard trying to get a signal into the computer....
Well, I might have burned it out, or then again, it might have been faulty already.
I bought an Optimus LAB1100 turntable, which has a diamond stylus and pre-amp, but is otherwise very cheap. From DSE, which is our local equivalent of Radio Shack, about US$70. It has a lead with RCA plugs, so you need a lead with RCA sockets to whatever your soundcard connection is. 1.5 stereo for mine.
I use LP Recorder, which was on a coverdisk, and Nero to burn.
Using the pause function in LP Recorder, you can record a whole LP into a folder, and if it is a short LP (they go from 40mins to 60mins) you can pad it out from compilation LPs, which you record into the folder first. Title each piece of the compilation carefully and include the running time (LPR tells you). As the CD blanks are 80 mins, you can get up to two LPs on a CD.

You are not making CDs with this method, just making the equivalent of taped LP copies, except playable on any CD payer. It is easy-peasey stuff, with any dust-crackles and clicks still in the recording, so keep Isopropyl alcohol and one of those dust-brushes handy. And if you play a game whilst recording, make sure the sound is switched off.