Computer starts but screen is black, only BIOS reset works

Hello!

For the past 3 months I've been having a problem that seems to appear only from time to time but now it's become serious.
I often get power failures at night because of my power supplying company and after one such failure my computer wouldn't start or, after giving it some time, it would start but with a black screen. Other times, but a lot less often, my computer would just shutdown and when trying to restart it I would get the same issue with fans running but nothing on the screen.

After a recent power failure, nothing would work, I tried leaving it off for hours, I also tried leaving it unplugged, the same thing would happen: fans start working, I can hear the power source buzzing but nothing on the screen. Sometimes the fans start running, then everything stops entirely, then it powers back on.

At one point I thought it's the HDD, tried unplugging it and the monitor came back to life but since there was no HDD, Windows didn't start. Someone suggested reseating the battery on the motherboard, so I did that and everything started working again. All this happened a week ago. Ever since, whenever I shut down my computer, normally, with no errors or anything, I can't turn it on again except if I reseat the battery. Any idea what's wrong and how I can fix it?

Sorry for the long post, but I wanted to be as specific as possible. Let me know if you also need system specs and whatever other info may be necessary.