2010 Dell Studio 1558 - Black screen, no output at all

Subject: Dell Studio Laptop 15" bought in July 2010. i3 -350M. Nothing altered except RAM (bought new and tested) and replaced stock HD with SSD 10 months ago. Never had any trouble except around 4 years ago, it would overheat and shut down. I air-sprayed the fan underneath, removed a LOT of dust and made sure such a buildup would not happen again. Other than that it always worked like a charm.

After the update to Windows 10, I experienced occasional freezes that required a restart. They didn't seem to be related to laptop activity. Sometimes I would find the laptop frozen after a couple hours of idling, other times it would freeze in the middle of something. They were random and far between so I accepted it as something that it did.

The real trouble started around June 20th. I was watching a movie with MPC-HC. The video froze with spurious pixels and the machine became frozen again. I didn't think much of it given its recent history and rebooted. I noticed that both the BIOS screen and the Windows loading page had spurious pixels too. Again, although this had never happened to the best of my memory, I didn't think much of it as for the rest, the laptop looked like it was loading Windows correctly. And eventually, as it arrived to the Windows Login page, it was clean and sharp, and after the login I could use the laptop with no problem.

The following day, as I turned on the laptop, the spurious pixels were still there - again up until the login screen, after which it was all clean and nice. That's when I started suspecting that something was wrong, although I could finish my work that day without a hitch. The next day, however, as I turned it on, the laptop went black -- no output of any kind on its LCD panel, not even the subtle backlighting that happens right after turn-on. I could hear the machine buzzing, the power-on button was lit, and after a few seconds the fan would start whirring, but the screen stayed black.

I followed instructions on previous posts. I tried removing the battery and keeping the Power on button pressed for 30+ seconds. I tried booting while keeping either the Fn key, the F12 key and the D key pressed, but nothing changed and every time the screen was black.

Eventually, as this model has a VGA port, I connected an external monitor. The laptop does show something on the monitor, but it's so fuzzy and riddled with spurious pixels and lines to be almost unreadable, although recognizable (the "Studio" logo, the BIOS screen if I press F2, etc).

So now, thanking you for having read up to this point, I would appreciate your help to determine what to do.

1. Did I report everything that is needed to diagnose the problem?
2. If so, can it be fixed easily?
3. If not, can it be fixed at all?
4. If so, what would a ballpark figure be for the repair?

Thank you again for the help you can give and have a nice day.