My Iphone5 won't turn on even though its been charging for hours

This has happened before. Every so often my ancient Iphone5 will turn off and be unable to come back on for sometimes days, sometimes hours, despite being fully charged. Is there a trick to get it to restart? Any troubleshooting ideas? It displays the iphone as needing a charge but I know its fully charged, its been plugged in for 6 hours now. Any help would be great.