Try to do a repair instal of your HD on the new computer. It should replace motherboard drivers with the proper ones. This is, with 95% certainty your issue. I've never done such a repair under 7 but you should find guides on it online (or even better, suggestions on how to swap HDD from computer to computer under windows 7 - I know preffered way is from sysprep but since your own computer is broken ...).
This however has the chance to permanently screw up your install so backup your HD first (clonezilla image - free, open source, great software to image full HDD). It's a fairly remote chance it'll screw your install but still there.
If it does work, you'll have to reactivate windows. If your license was OEM, you're screwed however.