DC-in, battery or board? Battery not recognised, boots with charger

Quick question: System does not recognise battery (have tried many things - not removing and reconnecting battery yet). Pretty sure it is a hardware issue as I did a system restore (downgraded to Catalina). How can I tell for sure whether there is an issue with the DC-in magsafe (cheap to repair so worth trying), the battery (replacing migh be an option) or the logic board (no way I proceed)?

More details if you care to read and help :)

Macbook Pro A1502 (EMC 2835) -bought late 2016- was working perfectly. No heavy use. During lockdown I brought it home and without access to my original charger I was using a spare one from an older macbook ( 60W magsafe1, i used a magsafe 1 to 2 adaptor). Had updated to Big Sur 2-3 weeks ago with no issues. All fine until one day the laptop could not charge. No liquids, no updates - just out of the blue. Pressed power button for long time - could only see a red battery symbol when charger was on. No other response, nothing when charger unplugged. I did SMC reset (system could not restart so no NVRAM reset).

Nothing worked -tried many things- until I did the following (found this in a post here - so thanks ifixit!): I pressed the power button for 10secs (with power cable off), following another 10 with cable on and then pressed the power button again- unexpectedly the system started!

Fans were running loud but system could reboot. I was able to install Catalina (with using a bootable usb -it took some time and fans were loud all the time) , in case there was an issue with the OS, did SMC and NVRAM resets couple of times. Issue is still here. Not sure if a clean install would help.

Now, the system cannot see the battery (as suggested in other posts) that might be the reason for the funs running constantly and loud. I had no warnings that there were issues with the battery in the past.

Anyone has any advice on what else to try? I am awaiting for a set of tools (don’t have a P5 screwdriver) to open the laptop. I am planning to disconnect the battery to see if the system will recognise it. Any help on how to do it properly? Will check if battery is swollen but I need an expert opinion on how to identify whether the issue is the dc-in (I could do it myself as the cost is low - 10 GBP/USD) or sth else.

No access to my office to get the original charger (due to covid), no apple store open here. How can I be sure it is the battery or the logic board? If it is the latter I will just leave it. If I am sure it is the battery I will probably get it fixed - not sure if I will try this myself mainly as I don’t want to mess with removing the adhesive.

Is there any way to tell which of these components is the issue ?

Many thanks in advance - Chris