Why won't my laptop turn on? Probably after overheating

Hi guys,

So, I've been meaning to change my laptop's battery for a while now, since it won't work unless the charger is plugged in (I don't know if that is relevant to what I'm about to ask). A few hours ago I was playing a game, and I assume it overheated...it suddenly turned off and I haven't been able to turn it back on ever since. The charging indicator is lit though. I tried removing the battery and then putting it back, but it still won't turn on.

Any suggestions?