BSOD while PC is idle, PC infected?

Yes, I just meant that I wanted to try everything I could before reinstalling again, sorry I didn't explain myself properly.

I upload here the CD screenshot.

I don't see where you've yet run the HD maker's HD Diagnostic which is required now to get a firm diagnosis on the HD.

If it's not fatal follow that with Disk Check run from installer Command Line, if necessary creating a full disk partition first using Partition Wizard or Step 2.2 in SSD - HDD Optimize for Windows Reinstallation

Do you have another HD you can run a test install using the steps to get a perfect reinstall?

Within 2 weeks, your drive's read error rate has worsened (I don't know enough to quantify how bad) and its "unstable" sectors count has gone up from 105 to 218. Definitely a bad sign. Especially if it wasn't due to something like a physical bump while the drive was trying to read/write, it's more like it's going out on its own. And if it is really going out on its own I'd be worried about rapid degradation.

As previously mentioned by other posters you should run the manufacturer's diagnostics program on the drive, and if the results dictate, use the warranty.

Backup first, get software inventory, license keys, etc. (before running diagnostics).

You should always have that stuff anyway...

Okay I will do that, but I have a quick question first. I don't know how to run the DOS diagnostic tool, when I burn the iso to the USB and boot from there it tells me to remove the drive and restart, like it can't read the application. Do you know any reliable way to run this DOS thing from a USB?

(I tried to use Windows USB/DVD tool but it doesn't recognize the iso file)

In cases like this you need to run the tool which specializes in writing a particular bootable app to stick.

What I would do is browse the bootable apps that are included on Hiren’s BootCD 15.1
and Ultimate Boot CD (UBCD) from a USB flash drive | USB Pen Drive Linux
which between them include nearly every diagnostics and partitioning (to check File System) app and can both be written easily to stick: Hiren's BootCD From USB Flash Drive (Pen Drive) » www.hiren.info