I got an elitebook 840 g2. Does just like everyone else's...9 times, etc. the trick for me for whatever reason is to unplug power, take out battery for a couple seconds, put battery back in, then press power button, then very very quickly plug power adapter back in.
If I plug adapter back in before pressing power button, all the lights flash. I have to plug adapter in a heartbeat after pressing power button because the battery is dead, but if I'm quick enough it will power up like normal.
If I power down the machine properly thru windows, it will power back like normal. If I let it go into sleep mode, then it won't power back up.
Maybe this will help somebody.