I had the same problem, went on a trip for two weeks, didn’t bring a charger, phone was completely dead. when I got home, I couldn’t turn on the phone even when it was plugged into the wall charger. it just cycled between red LED turning on and the charge icon showing on the screen.
I called blackberry tech support and it turned out to be an easy fix:
1. Plug wall charger into wall and then plug into blackberry
2. Take off back cover and pull the battery out (while it is plugged in still)
3. Wait 30 seconds. The red LED may remain on (tech said it didn’t matter).
4. Put the battery back in and wait about 5-10 seconds and it’ll begin to boot up (white screen with clock icon).
It may take longer than normal to boot up b/c battery was very dead. the tech support guy called this “jump starting” the battery. hope that helps you guys. it worked for me. no problems since.