SIL Rapidly Flashing, Not Powering On

If I press the power button briefly and release, the SIL comes on, then fades and the machine doesn't power on.

If I press and hold the power button, the fans can be heard spinning up, and the SIL flashes, dims, and then rapidly blinks. It sounds as if the machine is about to chime, but then abruptly stops and shuts off and seven seconds in.

My issue is pretty much as is described here and you can see a video from that post that is identical to my issue here.

I'm wondering what my next steps would be for troubleshooting this issue before I take the plunge and order a new logic board. I'm assuming this wouldn't be covered by the nVidia replacement program, either.

Thanks!