Seeing how the BIOS is outdated by 2 updates...I would most definitely update to the latest version. The next thing I would do is update the rest of the drivers on that PC from the link I provided in the previous post.
Other than that...if it's not supported for the next OS there's not much one can do. That's the risk one takes when going to an OS that's not supported...anything can happen at any time.
The only other possibility is the mobo itself....where the components that are attached to it has crapped out....eg the USB ports and the PS2 connection. The only way to check that out is to send it to a HP service center or find a replacement mobo for it.