First, I'm going to assume the mic uses a standard mini-jack that you plug into the sound card, not a USB mic. If that's the case, then it is probably not the mic. This is easy to test, just plug some headphones with the same kind of jack into the microphone input and see if the computer freezes (the speakers in headphones function much like a microphone, only in reverse). You could also try the same experiment with nothing plugged in to see if the computer still freezes. In either case you will have ruled out the mic if there is a freeze.
While it is most likely a hardware problem, I can't completely rule out a software glitch. It's difficult to diagnose this type of software problem because there are usually a number of programs controlling sound, starting with Windows, then any drivers/apps installed with the sound card, and finally the program you're attempting to use (eg. Skype).
I bought a USB headset for use with Skype and it seems to work fine, though I almost never use Skype or any other voice/video chat software. Be aware that USB headphones may not work with every app, for example mine will work fine with Skype or Win Msg, but not with Sound Recorder or any other audio program or games. But if all you need them for is chatting then a cheap set from Logitech may be a better option than replacing your sound card. Alternately, consider a USB audio adapter (
example), they seem to be very inexpensive, though I've never used one myself.
In the
I Feel Your Pain Department, I just upgraded my computer a few weeks ago, all I kept from the old computer was the case and one DVD burner, the rest is all new.

The single most frustrating problem I had was getting the sound configured correctly, I was literally cursing out loud at times. I like to use the stereo speaker out jack for my desktop speakers and headphones, mostly for games and music. I have the optical out (S/PDIF) connected to our 5.1 sound system, mostly for watching movies. Getting either one to work is fairly easy, getting both to work is a f#@king pain in the a$$. I've reached a point where I can do both, though I can't play a 5.1 source through the speakers or stereo music through the sound system without going in and changing the configuration. I can live with that.