Hi and welcome to the forums
Personally if the motherboard has been manufactured specifically for HP systems I think you will be lucky to find a non standard BIOS for it. Your best bet would be to check the motherboard to see if you can find some markings to indicate the manufacturer and model number, then see if Gooogle can come up with anything.
Bare in mind that the motherboard is unlikely to fully support all overclocking features as these were only included in the full featured chipsets which budget boards did not use. With a non K CPU you will be limited to overclocking the BCLK (Base Clock) which will overclock everything on you system (CPU, Memory, PCIE devices) so even if you are able to access BCLK you may not have great results anyhow if your other devices are not up to running higher speeds than standard.
You don't say how your PC is struggling, but have you checked the temperatures of your CPU and graphics card when under load? Either may be running hot and throttling your system in which case it could just be that you need to check and clean the appropriate cooler to bring performance back up to spec. Additionally it could be an operating system issue, so removing all unwanted software, running ADWCleaner & Malwarebytes, and then a using CCleaner to remove unneccesary junk, and clean the Registry (Scan & Fix Registry issues until all gone), may also boost performance.
Others may also chip in but hopefully that gives you some things to try.