Laptop turns on only on charger, infinite reboot

I bought this laptop used a year ago, and like a month ago I started facing issues. Trackpad sometimes was not clicking, keyboard sometimes did not respond - it was because of trackpad flex cable, and I used to fix it by disassembling my laptop and moving that flex cable a little. I bought a replacement, and was disassembling my laptop almost each day while I was waiting for the delivery. However, one day I was doing that same thing again and after I assembled my laptop again it refused to boot. Pressing on a power button did nothing, connecting MagSafe however turned my laptop on, only to reboot half-way through the loading bar. One more thing - as soon as I disconnect a MagSafe charger laptop shuts down instantly. I tried:

• Replacing old trackpad flex cable with a new one, laptop behaves the same;
• Booting without connected battery - MagSafe charger turns green then orange and laptop refuses to boot, pressing on a power button does nothing;
• Booting without connected trackpad flex cable - same behavior;
• Booting without anything connected to the motherboard - laptop still behaves the same.
• Resetting NVRAM and SMC - it proves that keyboard works now (with a new trackpad flex cable), though laptop still behaves the same way;
• Booting from a Linux live-USB - it tries to boot only to restart after some time, though that brief boot selector shows that after flex cable replacement keyboard and trackpad works without any issues;
• Leaving laptop with unplugged battery for some time - laptop still behaves the same way;

I don’t have money for a new laptop right now (though I already started saving). Is it logic board fault? I fixed a lot of stuff before and never experienced something like that. Google said that this laptop should boot without connected battery, and mine certainly doesn’t want to do boot without one. However, IMO that still looks like a battery issue - my battery is pretty worn out (not bulging though), but it was working before that disassembly. Only reason why I haven’t bought a replacement battery yet is it’s price - I don’t want to throw away that much money in case replacing battery won’t solve my problem.

TLDR: laptop used to work, after another disassembly refuses to boot on power button, boots only when charger is connected, only to enter infinite reboot loop. Disconnecting charger results in immediate shutdown.

Sorry for bad (maybe) English, this is not my native language and I’m writing this while still thinking what to do now. I hope someone would be able to help me. Thanks in advance!