I've been in the chat for the past while and found nothing so I figured I'd come to the front page.
For about 6-8 months I've had issues with my computer not starting when it was cold and even then when I plugged to many USB devices or a ethernet cable, it crashed, we eventually deduced the Power Supply was on its way out, so I order'd another one with almost exact same everything with the exception mine was 20+4 pin and this one is 24+4 pin, http://i.stack.imgur.com/5qpgb.png (Not actual hardware pictures just a diagram provided in chat).
Now with this one, warm or cold the machine has the same result, fan turns on, disc drive turns on, hard drive turns on, but the beep you'd get after everything powers on just before start is no longer heard, the screen receives no input and assuming it was perhaps a graphics issue, no audio you'd hear at start through the speakers is not heard.
If you place a disc in the drive, the drive clearly reads the disc.
EDIT: The Power Supply is ATX-250PA (1) FSP Group 250W 24 Pin and the desktop is ACER AM1100-E1401B.
EDIT 2: Copied from chat for a bit of ease, regarding issue with former PSU, displaying that the system does indeed start up. Ok me and Hennes have the same issue so I figured I'd do the testing, when our PSUs are cold the computer wont start, just tries, if we warm them up such as cranking the heat or using a hair drier to blow into the side vent for a min, they start up, with the exception of if you plug in to many USB devices it crashes and if plug anything into the ethernet port it crashes (just mine), so we deduced the psu was on its way out, since the USB ports draw about 1/6 of the power the ethernet adapter uses, we deduced the psu may not be able to put out enough watts for the system to run correctly, that and or there is a bad connection in the psu causing part of the problem (the whole warm/cold bit).