Do NOT under any circumstances connect the speaker connections from the all-in-one to the microphone or line input on your sound card... that's a recipe for disaster.
Are there any line outputs on the all-in-one (it would be useful to know who made the all-in-one, and what model number it is) ?
Ideally you need to connect 'Tape Out' or 'Line Out' from the all-in-one to the 'Line In' on your soundcard. If you don't have these outputs on the all-in-one, you may be able to get away with using the headphone socket, or some all-in-ones have a digital optical out (to go to minidisc) - you may be able to use this if your soundcard has a digital input.
Alternatively, forget about using the computer, go to E-Bay, and look for a Pioneer PDR-609 Compact Disc Recorder; should be able to get one for around £100 - £110 - this will accept either tape out or digital out, and works as easily as a standard cassette deck for recording from LPs
Regards, Graham