Usually tells me the motherboard is drawing too much power due to a short or other issue.

I usually start by moving the motherboard, CPU and HSF to cardboard leaving all other parts out for a power up test on cardboard with the PSU. If this works I check the case for extra mounting posts that over time can wear through paint on the motherboard and short out.

If it still won't power up then I unplug the CPU and go for a power up test. If that fails it's the motherboard or the PSU (rarely!)

The thing is that at this point you need spares to figure out which part it is.