Believe it or not, I just upgraded to Windows 7, myself, and encountered that issue.
On a tip from a forum like this one, someone suggested that I plug in the headphones and a microphone. Not having a headset, I got out a microphone from my stereo equipment that had the same size mic jack as the PC. I plugged it in. My headphones were already plugged in.
Oddly enough, IT WORKED!
I then closed Modern Warfare, then pulled out the MIC, then restarted it. It didn't work!
I plugged the mic back in, and it worked, so I just have the mic plugged in all the time now.
I was totally skeptical that this would work, but I think you should try it. I think I know the type of programming error that caused it. Windows 7 may have changed one or more multimedia instructions, making the subroutine that checks the mic work differently. A patch from Activision should fix this, but it's not a serious issue. Just plug a mic into the Mic jack, and you should be back to your killing.