Sorry, woodelf, no relation - it's my nom de plume on various platforms and comes from "Hellraiser" (LeMarchand created the puzzle box).
Re your original question, if you have a microphone on your machine try going to
http://www.midomi.com/ there is a "Click and sing or hum" button centre top. Click it and play your tune. Just tested and it correctly identified John Foxx's "Twilight's Last Gleaming", Abney Park's "The Wrong Side" and Placebo' cover of "Running Up That Hill", but not The Leather Nun's cover of "Gimme Gimme Gimme (A Man After Midnight)". Was no good for soundtrack selections, though. If still no joy, a "quick and dirty" way to get a digital copy would be to record the track with your microphone and upload it.
Otherwise, anyone with a mobile can dial 2580 and hold the mobile near the speaker of your tape player for around 30 seconds. They will be charged for the call (around 12p or so?) and if the service thinks it knows the track, it will send a text that costs 50p with what it thinks the track is.