How do I keep the operating system when upgrading a computer?

My little sis has a pretty old HP Slimline s7712n ( http://bit.ly/nD7wPf ), and ever since she started playing a few games, it just hasn't been cutting it. I'm trying to help her overhaul it as cheaply as possible, but I'm a little worried.

I'm looking at buying 4gb of DDR3 RAM, and either an A8-3850 CPU/GPU or an OEM athlon II x4 CPU paired with a Radeon 6570, along with a compatible motherboard. I can cannibalize an old Dell computer for a 450W PSU, a good fan to stick inside, and a good 19" LCD monitor. I can use the same Hard Drive and DVD drive, and use the stock cooler that came with my phenom II X4 965. Everything seems perfect.

But I just thought of a potential problem: The PC had Windows Vista Pre-installed. In the past, with my Dell Dimension 4600, I found out that Windows XP was essentially tethered to the motherboard. The Dell branded version of XP would ONLY work with Dell branded motherboards, and I fear HP may have done the same thing.

My question is this: If I switch out motherboards, will Windows Vista work with the new hardware? Are there any HP branded AM3 or FM1 motherboards that the Operating System will accept? I would rather not pay $100 for a new Windows 7 install, so is there any cheaper way to upgrade?