|Well, To get a successful POST (Power-On-Self-Test) on your motherboard you need only have Powersupply, CPU with heatsink/fan, One stick ram, Graphics and keyboard.|
At this stage it isn't possible for us to determine which of those components has failed. The symptoms you describe could be caused by either Powersupply failure or a motherboard problem.
The fact your onboard sound ceased working some time ago may indicate a motherboard problem or it could be just a driver corruption issue.
To begin open your case and do a visual inspection of the motherboard paying close attention to the many capacitors. Have any bulged or leaked?
With power disconnected, unplug and reinsert all cards & cables including Ram. Reconnect power and see if it will boot. Check that the CPU fan is spinning. If it has failed or is gummed up that would prevent bootup.
Goin' Fishin' (Some day)