It sounds like you may have a possible motherboard issue. I have seen similar behavior across many manufacturers and it’s usually a video card issue on the board. The fact that it eventually comes on is a new to me. It’d try a few things first.
Do you have your files backed up? If not, get them backed up.
Unplug the laptop and remove the battery. Try plugging in the laptop without the battery and see what happens.
If you have some spare ram to pop in, I’d remove the ram and put in some more ram to see if you have a ram issue.