Here's what I've put together:

Mobo - Intel Socket T (LGA 775) Intel G965 Express ATX
CPU - Intel Core 2 Duo E6700 Conroe 2.66GHz 4M sharing L2 Cache LGA 775
GPU - SAPPHIRE 100150SR Radeon X1900XTX 512MB 256-bit GDDR3 VIVO PCI Express x16
RAM - G.SKILL 2GB (2 x 1GB) 240-Pin DDR2 SDRAM DDR2 667 (PC2 5400) Dual Channel Kit
PSU - Rosewill 550W SLI Ready-ATX 12V V2.01 115/230 V
etc...

I put it all together, turn it on, the fans and LEDs go on, but got a blank screen and no beeps. I pull everything out except just the components listed above, still nothing. I put the RAM in different slots, one at a time, still nothing.

I replace the motherboard with this and get the same results, except that the CPU fan would rotate half a revolution once I turn the power on then stop, and when I power off, it spins a few revolutions and stops.

I tried plugging it into different walls, checked the monitor on another system, and unplugged/replugged everything.

So I figure it could either be the processor is bad (though I checked for bent pins), incompatible RAM, or the PSU is faulty somehow.

Any other thoughts before I set out to buy more hardware?

Have you connected the 4 pin from the power supply to the processor? You need spare parts to work with. Switch out the RAM and the video card. If you are getting beeps, remove the RAM completely and power on. If you don't get beeps telling you there is no RAM the MB is bad. Have you checked the BIOS reset pins to see if they are in the default position and not the reset position? Have you tried resetting the BIOS to default? do you have the power supply plugged into the video card? You may need a better power supply for that card you have. HTH.

Wow, I'm an idiot.

The very first time I built this, the voltage on the PSU was set at 115, but I had forgotten to insert the 2x2 ATX_12V plug. So naturally, the fans and LEDs died, so I figured, ah, 230V, not 115V!

So all my further testing was done at 230V, and only after I bought a new PSU (thanks for the idea, badge) that was not idiot-proof and proceeded to explode did I finally realize what I did wrong.

My original PSU thankfully still works, and I'm up and running.

Live and learn, I guess o_O;;