How can I recover iTunes from dead computer

You don't need to import or map drive letters or anything.
Quit iTunes.
Copy \My Music\iTunes\ folder from the old computer to \Music\ on the new computer.

We recently lost the motherboard in our PC. And, unfortunately, the backup that it thought I had diligently maintained was also corrupt. However, the old PC's HDD is perfectly fine. I now have it installed as a USB drive in a brand new PC.

I want to use the method mentioned above but I have a few questions. How will using these directions affect my ability to Sync the different iPods my family has (1 iPhone 3Gs, 1 iPod Nano 3G, 2 shuffles)? Yes, all of these were sync'd to the old iTunes. Will it be possible to get a full restore as if it was just the old computer when my kids go to iTunes? What about he music we have ripped from our CDs using iTunes? Will anything special need to be done for them?

Hold Shift and launch iTunes.
Select Choose library and select the *iTunes library.itl* file in the iTunes folder on the external.
That is all you need to do.
Everything will be there.
When you plug in an iPod, it will think it's a new library since the drive is in a computer.
Just select Yes when it asks to erase and sync.