Power / screen issues (No power to lid)?

My laptop, a 2013 Macbook Pro 15’ has been acting weird, and I am not quite sure what the issue is. I will timeline the events below.

Monday: I woke up and my laptop was quite hot. Checked it was sleeping and went to work. All was fine.

Tuesday: I woke up, hot laptop, so I made sure it was asleep when I left for work, and went on my way. Got home, dead battery. It must have woken and stated doing things and died. Plugged it in and started working fine.

Wednesday: Decided to check it before work. The display wouldn’t turn on at all, but it had a boot chime and the fans kicked in. There was also no light behind the Apple logo. Pure black screen. I tried numerous times to PRAM and SMC reset the thing, but that didn’t work. No video output when it is not displaying the screen or light either. I took it into a service place we use for work, they tested it and on the following Monday when I got it back they said the battery was needing replacing (which I knew, but was being lazy and not doing until I absolutely needed to). Other than the battery needing replacing, they said it ran fine. I tried to turn it on in the shop when I got it back and it was still playing up, no screen or Apple light. I showed them, they had another look and they said that it was probably a lid / screen replacement as well. I didn’t want them to do the battery because I can do that, and I said no to the lid replacement because it was going to be around 1k NZD (parts and labor).

Monday: I took it home and was starting to look for Macbooks to replace mine and decided to try turn mine on. It magically turned on. I took this opportunity to get my data off it. I let it run all night and it ran fine, not getting hot or anything.

Tuesday: Took it to work, started it, and nothing. Same issue, fans on and no screen / Apple logo light. Took it home, and it powered on in the evening fine. I downloaded Mojave, wiped the drive and did a fresh install. It was running fine all night, and into the next day.

Wednesday: I restarted it numerous times to test it and it was all looking positive. I tried it a bit before lunch, back to being problematic.

I have ordered a new battery for it anyways, and will do the swap, but does anyone have any clue why it’s doing what it’s doing, and how to fix it? I really don’t want to have to buy a new laptop if I can avoid it, nor do I want to spend thousands on a 2013 MBP, but I also don’t want to have to get a new laptop. Also, what are the MBPs worth as parts? If I need a new one, I will sell this one as-is for parts.

Thanks for reading and in advance for answers!