I have used the free Paragon Adaptive Restore boot CD to successfully move a Windows 7 hard disk to a different machine at least a dozen times, often even between AMD and Intel.
You install the hard disk into the new system, making sure not to boot from the hard disk, but instead boot from the CD. After booting from the CD, it will examine the hard disk and the new system hardware. It will then remove incompatible drivers from the hard disk and install compatible drivers for the new hardware. It also takes care of the HAL and Windows keys/registration.
Of course, you should clone and/or back up the drive first, so if something goes awry, you have a back up.
Personally, I would repair the motherboard or replace it with an identical motherboard sourced from eBay. You should note that the capacitors on the motherboard generally fail because of noisy input voltage, which is usually caused by the capacitors in the power supply failing. If the power source to the motherboard is very clean, then sometimes the filter capacitors on the motherboard are not even needed for it to operate. I have actually had motherboards with bad capacitors that I needed to get operating again(just long enough to back up the data on them) come back to life just by replacing the power supply with a new one, and physically breaking off the dead capacitors on the motherboard.
You can also replace the capacitors on the motherboard. It should be noted, however, that proper replacement requires better soldering/desoldering tools than most people have, as the ground plane layers in modern motherboards that the capacitors are soldered into absorb a great amount of heat, to the extent that they are very difficult to properly remove while leaving an ample hole in the motherboard in which to install the new capacitor.
If a person were desperate enough, the capacitors can be physically removed from the motherboard by tilting them sideways until the legs of the capacitor pull out of the bottom of the capacitor, leaving the leads sticking out of the motherboard. New capacitors can then be installed by trimming the leads of the new capacitor to around 5mm, and the new capacitor then soldered to the protruding leads from the motherboard. Note that when physically removing the old capacitors, the remaining leads will usually have an aluminum cap on the tips of them which cannot be soldered to, so the aluminum tips have to be cut off first.
