F12 doesn't work (I have used this function on this computer many moons ago)
The below explains why pressing F12 does not work.
There seems to be no response to unplugging etc. and now the lights on my keyboard don't turn on when I press num lock or cap lock.
Suggests that the keyboard itself is not working, this can be caused by the USB ports either getting no power to them from the MB or the USB ports being disabled in the BIOS somehow.
Yes the buzzing, none working keyboard and the problem/s in general could all be related with one such culprit as the cause being a flaky PSU.
Your computer should have four diagnostic lights on the front, if yes, what sequence of LEDs do you get when attempting to boot up, see light patterns here
If the specs that I have for your computer are correct you have a Radeon X600 add on video card, the MB has Intel integrated graphics but no PS/2 ports for a wired keyboard meaning you are using a USB type keyboard, are these specs correct.