audioguru- You are the audio guru of course, although on my own equipment I've always risked it without problems. Ah, and perhaps aren't modern sound cards' single inputs combination line-level/microphone? (Not the mega SB live stuff, just your cheapo stuff)
I'd still just do it the simple way myself if it was my stuff. Ok, so you need a $2.00 1/4" to 1/8" adapter for that headphone jack. (Don't you have any lying around? It's really not a rare or "special" size.) And then you still need the very cheap male-male cable I mentioned. This has the advantage of being very convenient, and the parts can likely be found in your local megamart.
But anyway, no, the microphone connection on your computer only needs 2 contacts, not 3. You were likely thinking of more high-end mics with balanced connections, used in more professional settings and such.
If you still would like to figure out which two wires go to the appropriate plug on that combo cable of yours, that's easily done by using anything rigged up as a continuity tester, such as a battery, couple wires, and a flashlight bulb or battery tester.