Hello
Stefano G. I'm sorry to hear about your PC problem. The fact that the power stays on, meaning the system doesn't restart nor shutdown, leads me to suspect that your GPU is the culprit.
Do me a favor: Open the side panel of your computer, so that that you can spectate the fans on your R9 280x. Turn on your computer and take a glance at the fans, and make a mental note of whether they are spinning or not at that moment, while booted into Windows. Most likely they won't be spinning while in Windows, since they'll be in 2D mode. Then launch one of the games that you previously attempted to load, and see whether all fans are spinning.
My best guess: I suspect that at least one of your GPU fans is no longer spinning, causing your GPU to overheat, and the image is shutting off as a failsafe. Is one of the fans snagged on a cable? I suppose that excessive dust caked around the GPU could possibly cause this issue or even the stoppage of a case fan.
My 2nd request: Could you please take three photos, upload them to imgur and share the links here? Photo #1: The entire inside of the case, to show the air flow. Photo #2: The label on the side of the power supply, to show the precise model and specs of your PSU, in case my theory about your GPU overheating is wrong. Photo #3: A photo of the computer with the side panel replaced, with the computer in it's original position in your home. I'm wondering if air flow to your components is restricted by being placed inside a desk cubby or something of that nature.
Question: What is the exact model of your R9 280X? e.g. MSI R9 280X Gaming 3G. I'm asking in order to research the default fan behavior of your GPU, and it would also tell me your official power usage.
You can download and run a utility to check your GPU temps.
<scroll halfway down page> and <click> Setup English
HWMonitor for Windows® x86/x64 is a hardware monitoring program that reads PC systems main health sensors : voltages, temperatures, powers, currents, fans speed, utilizations, clock speeds ... The program handles : CPU and GPU-level hardware monitoring...
www.cpuid.com