Do laptop power adapters fit in here ?

A question: If a laptop shuts down in a sudden, is it due to the adapter or the components in the laptop ?

Hint: LED on adapter shuts off as well (most of the time)
Hint 2: LED on adapter stays lit (very rarely)

Went to shops and they don't know a thing about this (young technicians).

Plug off the power, plug it back in, adapter is on (LED is lit), and laptop on as usual (no software probs whatsoever).
Stays on for depends, on a lucky day >48hrs, right now on for about 15 mins max only before shutting down again.

I believe no, since I bought the laptop (used) with the battery not functioning at all.
Laptop will not power on without adapter.

Adapter does not charge that battery too.

However it has been that way for many years now (5 years) and just recently having this problem.
Before that the laptop performed very2 well without issues.

Reason for not removing the battery because it was part of the laptop's body (see pic, bottom left is the battery)


If removed, the laptop is not stable.

Any advice ? Appreciate your help and time