What is the best c p u-mother board combo for gaming?

Win an OEM motherboard and operating system, you are limited to a 'parallel' move to a similar chipset (for maintenance of the damaged component) under the terms of the OS EULA (end-user license agreement).

What model is you HP desktop?

What that means is a meaninful upgrade of the motherboard will include a new operating system. (ie operating system [Windows 7?] is legally locked to original or similar motherboard)
A Video Card upgrade is possible and desireable. The Difficulty is discovering what the board/cpu combination will support and the limitations of the OEM power supply.
Memory is also a consideration, as is case cooling if you add a Video Card that operates at high wattage.
What is the model information?

I found out that it was more cost-to-performance beneficial to just build a completely new computer at this point. Now my old HP C2D is my secondary PC...