Homebuilt with maybe not enough power from the supply anymore to handle various upgrades done? I would put another powersupply on a table next to it, plug it into the motherboard without removing the other one yet physically, and see if it boots up with the spare by not hooking it up to anything but the board itself with the connectors and maybe the monitor. If still no beeps, remove the ram sticks and reseat just one at a time in case it's got dust or debris around the slots.....
If still no beeps, think CPU....is that fan working? Even if it is, remove and reseat the CPU and hsf and try booting again. Normally for me, if no beeps, it's the CPU or the bios/cmos jumpers reset to OFF and then ON again after about five minutes to see if the bios needs to be reset to defaults in order to boot it up.
Those are the areas I would start at first.
A friend said her PC is eaten up with popups and junk. Asked me if I could fix it. Sure I said. It's probably infected with parasites.
I get it home and on a cursory inspection I see that it's a home built with a DVD ROM, floppy, and an internal Zip-100, unknown size HD. I plug it in and press the power button. The Zip drive LED flashes once, then nothing. The power supply fan is running, and removing the side panel I see the processor fan running. But nothing. No beeps, no video, no nothing. It does have three RAM sticks of again, unknown size.
Since my systems are perfect, I've never seen this type of behavior.
Where do I start?