
Modder had used lead free solder and no flux and the joints were not fully cleaned so a lot of the solder blobs were clearly a mix of leaded and unleaded solder. The DC jack was corroded and needed some scraping and cleaning.
Here are pictures of the initial partial teardown I did:
Spoiler








Last week I finally found time and motivation to fix the unit up. I replaced the screen lens, managed to remove most of the dust from the housing and screen, but failed to fix the diffusor debris. As I fully disassembled I noticed the previous owner had broken quite a few screw posts, like one of the cartridge slot screws was just held in by electrical tape. Kinda worried that cart insertions will put strain on the mainboard :/ One of the screw posts for the diffusor / LCD mounting bracket was broken and there was a hairline crack in the diffusor. I couldn't get the dirt out the way it got between the LCD and diffusor and I didn't want to separate it from the LCD as it seemed like it might fall apart. Guess I could always remove it and install an LED back light.
Here are some more pictures of the case damage and a front shot of the motherboard:
Spoiler


I could reproduce the issue with different games, no game, official PSU and batteries, so nothing external was causing this.
I asked and googled around for troubleshooting steps and decided to start with the power board. I took it out and poured IPA into the switch and moved it around a few dozes times, repeated that cycled a few times. Switch got a lot stiffer to actuate for some reason. It is next to the corroded DC jack, reasonable to assume it also has some corrosion. The switched measured <1 Ohm for closed positions and >2 MO for open, seems good. I also replaced the solder on the replacement capacitor joints. I measured all caps with an in-circuit ESR meter. Looked all good in terms of capacity & ESR, just the largest cap had a capacity reading an order of magnitude too high. These in-circuit meters are not reliable anyway, I guess. I checked all the voltage rails without a load, looked good to me.
Initially it seemed like I fixed it, didn't get anymore boot failures but after ~15min of testing I had console resets again. Next step was re-doing the crappy solder work on the re-cap job:

Here are full pictures:
Spoiler







I again though that I fixed it but after ~10min or so I again had in-game resets and then repeated power on failures. This time I noticed the power LED was blinking. Never seen that before, apparently that's the GG signal for low battery, so voltage must've dropped.
At this point I'm not sure what to do. The issue seems to be that either that the power board can only barely deliver what is needed and the console eventually shuts off due to some kind of low-voltage brown-out protection or there's something on the main board failing causing excessive power consumption and triggering a fuse or some other kind of over current protection.
Thanks for reading all this, I wanted to include all details. If you got any idea how to fix or diagnose this, please share.