Here's what I would do first, if you haven't already:
Start with the following:
-Motherboard
-CPU & CPU heatsink
-1 stick of RAM in first DIMM slot
-Video card (unless the motherboard sports integrated graphics, in which case leave the Radeon out for the time being)
-Power supply
Set the motherboard on a non-conductive surface (I favor the motherboard box, but anything non-metallic or wet will do the trick. This way, if there's a short in the case, it won't interfere.
Install the CPU and it's heatsink, making sure the fan is plugged into the CPU fan header. In some cases, the system will not boot if there's no fan RPM detected from the CPU fan header.
Install the video card IF there's no on-board solution.
Clear CMOS. If you can't find the jumper, pull the battery out for a few minutes and reinstall.
Plug in the power supply to the motherboard, ensuring all connections to the board are plugged in.
Use a flat-headed screwdriver to short the power switch jumper (consult the manual for which set of pins) and the system should power on.
This is a minimal configuration to help narrow down the cause.
If that powers up without issue, begin the physical installation of add-on cards, one at a time.