If your computer won't start, of course it's serious - you don't have the use of your computer. But the solution could be very simple. Or not.
SMC resets won't hurt anything, and they won't affect your warranty status. If you called Apple for support, I'm sure they'd ask you to try the SMC. If it's still not starting up, then take advantage of your warranty.
This Apple support article may help:
https://support.apple.com/HT204267
It's at least possible that your SMC reset was not successful - pushing all four of those buttons at the same time isn't all that easy. If you haven't already tried holding the power button for at least 10 seconds, try it - the system may currently be hung and needs a restart.
The system (actually, the batteries) will get warm when charging. The question is when that becomes abnormal, rather than normal. However, an SMC reset isn't likely to fix anything of that sort. If you think it's abnormally warm... again, that's what an warranty is for.
Meantime, if you're not seeing lights on the MagSafe connector, make sure you have the other end connected to a working outlet - at the moment, it's at least possible you have a dead battery AND a disconnected charger. Check the connections, try a different outlet, borrow someone else's charger if possible.