Laptop screen full of static- Is my computer broken?

A week ago, as I was using my computer (it is a Lenovo, can't remember what model at the moment) the screen suddenly flickered and went full static. The static is white with some color on a black screen. Sometimes the static moves about, cycling, and other times it just freezes up.

I killed the power and tried again but it still did it, so I shut down and let it rest for half and hour. When I powered it back up everything was fine and I assumed it was a glitch.

Now, just today, the same thing happened after I left it unattended. I have turned it on several times in a short timespan but it still has the strange static. I also tried connecting it to another monitor but the monitor does not show anything, leading me to believe this is a problem with the laptop itself.

The laptop is roughly 3 to 4 years old. When I opened up the bottom I found that the fan was coated in dust and the laptop did feel warm to the touch. I know that my brand of laptop does have issues with the fan and heating issues.

My questions are as such:

-What exactly went wrong? What broke?

-Was this an overheating issue or age?

-Is the computer completely broken or is there a replacement piece I can get? Should I even do that?

I can afford to get a new computer but would rather not, obviously. I have backed up almost everything on it, so I'm ok there.

It could be The drivers that run thew screen itself. I used to have a toshiba laptop that would have a static like effect that would happen at random. Maybe investigate or update drivers?