WEll, just because the CD Driver and such works with the new PC, doesn't necessarily mean the RAM will. The thing about RAM is that if it's not compatible, it won't even fit in the slot, so you can pretty much tell really quickly if it won't work. Unless, of course your going to an older machine (not sure why you'd do that, though). In that case if you had (for example) 1GB of pc 3200 RAM, and tried to put it in a machine that would only handle PC 3200 512 MB, then that's gonna be a problem.
But as long as your putting it into a newer machine, and it fits, the RAM should be OK.
As far as the HD, just hook it up to the new one (like a daisy chain), and make sure to set up your BIOS so that it boots to the HD you want... Might take a little bit of playing with it, but either HD should be accessable from your PC OS as long as you have it hooked up correctly.
A good example of this is when I put a VERY OLD HD into a bran new PC at work. The darned thing only had like 10 GB on it, but it had ESSENTIAL software for the prepress department of a print shop. The RIP software used a dongle to prevent pirating, but the old HD worked in the bran new machine nontheless.