Re: New build startup
Test your RAM out with MemTest x86, or grab Hirens Boot CD, it has several diagnostics software titles to pick from on there.
You can use any installation media for Windows 7 on any PC, but the CD Key is what matters. If the CD Key was "OEM" in that it shipped with the original PC if you bought an OEM system from Dell, HP, etc, then yes, the CD Key is tied to that hardware. If you bought an OEM copy of Windows, it's possible to transfer the CD Key, but it's not supported. I only mention it because I've seen people do it, though it's rare. (You have to make one hell of a good excuse...)
If you buy a retail copy, then any PC you install it to, as long as you don't exceed the number of licenses installed (1 or 3 PCs, depending on edition).