Try this: plug the device in for an hour or so, then unplug it and leave it for another hour and then plug it in again and leave it for 24 hours. A flat battery needs to be coaxed back into life. If that doesn't do anything, the phone will have to go for repair, I'm afraid. Sometimes you can't get a flat battery to charge at all. I did recently have to revive a flat battery, though, and it was about 2 hours before the charge indicator came on.
It's a very bad idea to allow any lithium-based battery to go completely flat as it'll shorten its life. Generally, try to turn off at 20% and top the charge up whenever you can. There's not memory effect and top-up will do no harm at all.
