Dim Power Light - Computer Won't Turn On

A few months ago I bought an Alienware X51 R3 from Dell. It worked fine, but occasionally had weird issues, despite being a new powerful gaming desktop.

But starting yesterday, I came back to find it seemingly shut down. The power light was on, but the screen was black and the system seemed to be sleeping. I touch the power button, and nothing happens. Clearly it was already shut down, but I never told it to do that, and only left it for a few minutes.

I tried to turn it back on, but now the system does not boot, or even try to. The fans don't power up, the lights don't even turn on. The only thing that comes on is the power light, but it's dim. I have never seen that behavior in a computer before.

So, I made sure to disconnect the power supply and hold the button for 20 seconds, to make sure the charge was drained. Still the system won't power on. I turned on the monitor, but it works fine. The system isn't even trying to power on.

After doing my own research into the growing list of problems with the X51 desktops, there's a particular issue with the graphics card that comes with certain versions.

The GeForce GTX 970 card in this desktop seems to be prone to stop working, at least that's what I've seen in the problems reported by other costumers that ran into the same set of problems. I don't know for sure if that's the problem here, but the brick for the power coord still shows its own light when plugged in. It seems to be working on that side.

Did the power supply malfunction in my desktop, or is the video card dead in less than a year of use? I don't know who else to ask, because I can't seem to find Dell's online technical support chat now, it always redirects to a series of automated questions that aren't helping with my problem.