I never ceases to amaze me the amount of time a PC is turned off only to find it won't start the next day ... and I am not surprised anymore to find that the PSU had died.
That can be one aspect, and just because the fans work don't mean much to me.
No beep = MB failure, usually ... I suspect the MB for another reason also, It asking you to enter BIOS ... are you using a USB keyboard, if so, go get an ordinary KB ... you should be able to enter the BIOS with that, if the MB is OK that is.
Not much one can do if you cannot swap-out parts for known good alternatives.