You're very welcome.
The Intel graphics driver from the 8300 Elite supports the Intel HD 2500/4000 onboard graphics, doesn't it?
See Page 5 of the quickspecs.
http://h18004.www1.hp.com/products/quickspecs/14268_na/14268_na.pdf
PROCESSOR
USDT SFF/CMT
Intel® 3rd Generation Core™ i7 Processors
Intel® Core™ i7-3770 Processor
Up to 3.9 GHz Max. Turbo Frequency (3.4 GHz base frequency)
8 MB cache, 4 cores, 8 threads
Intel HD Graphics 4000
Using the wrong drivers shouldn't result in any damage to the PC.
They just won't work (install).
As I see it, you don't have much choice except to experiment.
Your PC is not supported for XP by HP, which is why there are no drivers for it.
I do not believe the Intel 4000 HD graphics driver from Intel will work.
The chipset driver will also include the drivers for your H61 chipset.
Before we have to start looking helter-skelter for drivers, I wanted you to try the drivers from the closest matching PC that could be found in one convienient place.
If one or more of the drivers don't install, we will have to start looking elsewhere.