New pc mini freezes help

Install CoreTemp and GPU-Z and get them to log your temperatures.
Also, you may have bought a cooler for your CPU, but you did also remember to get thermal paste right?

check for a bios update. @bios is super easy to use.

PSU?

I guess not-enough power on full usage situations (like gaming) but we really cannot help you based on just "some beeping sound" - you should run full diagnostics soft while playing games to find what the actual issue is, as it can be nearly everything (different mobos have different beeps for different things).

Maybe it's the StickyKeys thing where you press a button a bunch of times in a row. See if it pops up when you press the Shift button really fast like 5 times. It might come up when you play games.

Could you check the specs for the PSU as well, please?

If you have the restore point, try reverting to old drivers, then try the games. Then install one new driver at a time and test the games again.

Under BIOS Setup Utility > Advanced tab > Chipset > Southbridge configuration > Primary Graphics Adapter. Choose the option [PCIE -> PCI -> IGP].