lol.
this is a common problem with a lot of phones.
its not really a "problem"
its that, the battery gets to a certain point and the phone shuts off, but the software cant always tell where a "safe" point is to turn off the phone. the ideal method is to turn it off when the battery is low enough that it can still turn on once its plugged into power.
sometimes the way the software calculates how low the battery is doesnt work correctly, so if the phone thinks the device is at 5% but the battery is actually closer to 1%, then the phone shuts off when the battery is truly dead and it wont turn on.
when you plug in the phone from a dead state, it recognizes a charge, but uses the batterys own power to turn on and enter the OS if possible or the recovery firmware (that battery charge screen you see when a phone is not booted into android but still on and charging)
when it seems like the phone wont turn on, its becuase it cant start up under its own power. that doesnt mean its broken, its still charging even if you cant tell.
the best way to fix this is to keep it plugged in, walk away for an hour or so, come back later and bam! it will be on!
I've seen this happen on way too many phones and other devices for it to be an issue.
yes, it happened to my triumph, it was low, i fell asleep, woke up totally dead, wouldnt start or do anything. plugged it in and didnt start either. I almost, ALMOST panicked for a second until I remembered this happens to a lot of devices.
I left my phone at home, went out to eat, came back 2 hours later and it was charging and loaded into android.