Switch doesn't turn on when left joy-con is attached

I have a rather peculiar issue and am uncertain if my assumption is correct. The console was purchased second-hand, so I am not entirely sure what happened.

Initially, I discovered by chance that the console only turns on when completely powered down and the left Joy-Con is not attached to the console. (at this point, I didn't know, that the Joy-Con was the issue)

Since today, I've also had the problem that the Joy-Con charges but is no longer recognized in handheld mode.

After cleaning the contacts, the Joy-Con seems to work normally in handheld mode again, but now I have a problem with turning it on. I was able to get it to work without any problems for a while, but unfortunately that's no longer the case.

Would replacing the left rail help in both cases?