There are a few things I'd like you to try.
First, pull the battery out if you can, and plug it in. Does it boot?
Can you boot into recovery? If there's any SD or SIM card, pull those out and try again.
Pull out the battery and leave it out for a good amount of time (couple of hours, to try and clear the cache).
Fully let it charge without trying to turn it on, if you can. Then unplug it and try again.
I've heard of some bootloops after battery dying caused by software, corruption of some files or partitions when the battery died. Those can be fixed.
Best of luck, report back with any developments.