Step 1: Swap mobo
Step 2: SysPrep to create an image
Step 3: Re-install using the SysPrep image
To be extra-clear and re-emphasize what Ryu Connor is telling you, the "image" in your example is the installation on you harddrive.
In other words,
1) Boot from the original harddrive using the new motherboard (this should almost certainly work)
1b) ...Once Windows 7 is done discovering everything and the computer is usable...
2) Run sysprep (following Ryu's detailed instructions, which will automatically turn off the machine for you)
3) Just turn the computer back on (and follow the rest of Ryu's instructions).
You don't really have to "re-install" or "create" any images, sys-prep is automagically cleaning up/preparing the only image you're going to need to deal with: the pre-existing installation on the HD!
As Ryu points out, don't listen to all the ridiculous FUDsters. The *only* hiccup here is the fact that the original motherboard is kaput, but so long as you can boot into windows 7 (which you should be able to), that's easily surmountable. This isn't crazy-talk. I've done it, and people are routinely doing it everywhere. I'm not sure why people think it's impossible/dangerous.
Best guess is that all the silliness is coming from the days of Windows XP, which wouldn't allow you to do what you're about to. But as Ryu says, that hasn't been been the case since Vista.
You can verify what he says, as usual, so there isn't any sense in even taking a vote ;P