you should check the POWER OUTPUT voltage the UPS is giving.
seems like ur SMPS might not be getting the correct input voltage. connect directly to the wall plug and try to regenerate the problem. if none then ur UPS is faulty.
It could also be your power switch gettting lose or stuck or dust inside it, or the switch to mobo wires are loose.
Also see if ur BIOS is seated properly(if it is not soldered on the mobo). try to reflash it with the latest bios image.
Reseat your RAM and CPU both after cleaning their contacts with a paint brush(dry ofcourse

). also clean the slots where they go in.
See that your heatsink has thermal paste.
Check the ATX power connectors. they might be loose or damaged(by accidental pulling of wires etc.)
Last of all disconnect everything from ur mobo other then the display, ram, CPU, power LED, SMPS. NOw identify the power PINS and short them with a piece of wire or screwdriver. if the system POSTs then try again till u r satisfied. Now start connecting stuff one by one and keep checking for power up faliures . as soon as it starts to fail then u know the problem.
if shorting the Power Pins on the mobo give same trouble then start replace all connected components(cpu,ram,smps,mobo) with good working ones untill it gets ok.
That should be it.