I have a computer, a Dell Optiplex 755, that turns itself on whenever it is being supplied power. It turns on, and all the lights come on, the fans spin, and the monitor does recieve input, but it's just a black screen. I get no noises or beeps or a POST or a BIOS, I get absolutely nothing, just a computer that looks like it should work but doesn't.
Every time I've experienced this it has been a bad power supply. Look at the diagnostic lights. More info from Dell here.
I've seen this happen when there's a bad spot in the first dimm or low in the addressing scheme of the second. I've also seen this when the system has a non bootable thumbdrive attached and the system is set (bios setup) to boot from usb devices before hard drives. I've also seen it when an attached external storage usb device has gone bad. this could be an external backup disk, or sometimes a printer that has usb disk emulation software like the hp p1606dn. So detach anything usb other than mouse and keyboard. then power up. if this fails you, then try unplugging the power, removing dimm 1 and dimm 2 and moving dimm 3 and dimm 4 to the slots for dimm 1 and dimm 2 before powering back up. good luck.
I see this is old but I'll comment anyway with my input...
I have a Dell Optiplex 980 and I was installing 2 new sticks of RAM, 2GB each.
I had a problem with the 2nd stick, the monitor won't turn on with the 2nd stick in slot 3 or slot 4. However with the 1st stick in slot 3 it's fine.
When I booted up I pressed F12 for startup options and went to system, from there I could see bios logs (bottom option) and in the log was an entry about intrusion into the motherboard. I wanted to add this in case it's useful to anyone else who might want to view their logs.
Without the bad stick and with one new good stick, the bios reported memory size changed, then booted the operating system ( Win 7 64 bit ), and the extra memory seems to work fine so far.
I took out the memory (RAM) card, blew on the slot to remove the dust and reseated the card. This resolved the issue for me