I didn't realise ths post wasn't dead yet after posting a few days ago with no reply. Anyway, here is why i repost:
I was thinking afterwards about this for some reason and something clicked:
I was thinking, overheat, power suply blew, obviously power suply of a laptop is the battery, and that can't "blow" as such, but can cause stuff to break.
Like a normal desktop PSU all new laptops come with a multitue of power suply protection, such as over voltage, under voltage, short and (this is the one i want to draw your attention to) overheating protection.
What happens is 2 things:
First, you have a little component in your laptop that is the same as a little compnent in a desktop power suply. It is a tiny little black thing that is soldered to the PSB in the PSU. This is the overheat protection and when your power supply overheats (in your case, laptop so battery) this blows up, litteraly reaches a certain temperature and goes bang. It goes in such a way that it damages nothing else in the system, obviously the PSU is screwed, but it stays contained. This why when a power suply overheats and blows, you hear a pop or bang sound.
When that happens, the second thing happens. It causes the fuse in your power supply to fail, shutting off all power becuase the circuit has been broken. The circuit is no longer whole and so no power can reach the system, this is why it would not turn on, or why i would imagine it would not turn on.
Take it back to whoever sold it to you and, provided it is under warrenty, they will take it off you for a day or 2, find this out for themselves from looking it over and replae your battery/other part with this fail safe device, or give you a completely new system