Jon, I have a very cheap Optimus LAB1100 turntable (not my main one I hasten to add) and it connects effortlessly to this W7 computer and its CD burner.
The unfortunate part is that I don't want to burn CDs from my LPs, nor to listen to the results on the computer speakers, but to listen to them at the noticeably higher quality that LPs offer.
-Providing you've looked after them. And burning copies is a tedious job anyway.