It can be possible, however:
Sometimes it will not, simply since its a big change in hardware.
Your system already knows how to use its current hardware, and will attempt to boot like its using the same hardware, therefor, a complete change (usually the motherboard change is the biggest problem) may result in it not being able to be used
Still, some other things need to be considered:
Do you really want to go without doing a complete cleanup? Using your current instalation, which by now, is probably cluttered. You should start new with a new computer, to make sure everything is running as fast as possible.
Do you really want to use a old hard drive? Your getting a new computer, with a hard drive in it. Why not set up your old drive as a secondary (sometimes called a Slave drive), an the new one as primary. This way, you have access to your old stuff (and can copy it to the new drive) and you can use the second drive for backing up stuff.
So, the answer to your question:
It might be possible. It just depends
Second question:
You added new RAM to your old computer, and it fried the motherboard? I dont think this is possible. Incompatible RAM will just prevent the computer from booting, or will result in random BSOD errors
I think you might have fried it. Next time you open up your computer, follow these precautions:
http://www.computerhope.com/esd.htm
