Backlights won't work when keyboards and mice are plugged into PS/2 ports, as they cannot provide as much power as USB.
Can you get into the BIOS with the keyboard plugged into the PS/2 port?
4 beeps mean 'Timer not operational - bad motherboard'. So I'd advise returning your motherboard for a new one.
https://forum-en.msi.com/faq/article/bios-beep-codes
As for the other motherboard, do you mean that it turns on and then a couple of seconds later, turns off?