MacBook Air will only turn on with Magsafe connected after a while

I charged my Air overnight and when I tried to turn it on in the morning it didn’t boot. I tried plugging in the Magsafe in to find that no light came on. Doing an SMC reset didn’t work. Later on, I had the MagSafe plugged in for over an hour and the orange light came on, and pressing the power button turned it on, albeit it, was very slow. If I unplug the Magsafe cord, after 5 seconds it abruptly turns off.

I doubt it would be any water damage, since I haven’t spilled anything on it, nor was I in a humid environment. Potentially the battery might have something to do with it; the “Service Battery” notification came up the day before, although it seems to charge just fine, and as I type this, says the condition is “Good”. My research says that it could be a bad Magsafe connection.

Any help would be awesome.

EDIT: Screenshot attached of CoconutBattery, doesn’t seem to be a battery issue, although 711 cycles does seem a bit extreme. I’ve also noticed that the MacSafe brick and the Mac itself is scalding hot, if that is any help in assisting. The male and female MagSafe connectors are free from debris, the MagSafe connector is about two months old, the other one broke after 4 years.