I know you said that it's not a hardware problem, but there is a lot of hardware on a computer. Hear me out.
Try these suggestions, just to see if one of them works for you:
1) Attach a flat screen monitor, or even any video screen, and see if you can get dependable performance, without the problems you are experiencing.
2) Plug in a USB flash drive. It could be any usb flash or external hd, but stay away from usb devices like a printers or bluetooth. This might bypass a possible faulty motherboard circuit, and cause the video to start working again.
3) Try running on just battery power. Again, faulty circuits could be bypassed by not using the A/C circuits.
If suggestion 1) works, it's possibly a bad video backlight inverter. I used to repair computers for a living, and I repaired a couple of these. The screen goes completely dark, intermittently, but you can actually see what's on the screen if you shine a flashlight onto the screen.
Take a look at this video, which shows how to replace the backlight inverter:
https://www.youtube.com/watch?v=ucaJA324hbg