I have a couple of Samsung 10" tablets - one old and one newish. The newer one I let run flat and after charging it, it wouldn't turn on - turns out these tablets don't like charging flat batteries. After a lot of searching (and why I'm posting it here) I found that holding down the power key and down volume (for 10+ seconds) whilst plugged in forces it into charging mode. I'd left this on charge for two days prior to this without any success - actually thought it was bricked until I came across this simple solution.
Mike.