Whenever you change the motherboard, Win will detect the change the next time it "calls home". You will have to re-activate to keep from getting the perpetual nag screen. If you bought Win7 retail, the key is on the package it came in. if Win7 was pre-loaded on the PC, it should have the key on a sticker on the machine somewhere. W/o the key, you have no proof you have a legal license. Sorry.
Yes, you can always re-install Win7 on the bad drive. But that won't fix the missing key problem.