dead 5s
My 5s has gone dead on me after not charging my phone for 6 weeks. I was away holiday and didn't won't to use a 3rd party charger. Got back, got myself a new charger and my 5s won't start.
Leave it plugged in for a minimum of 1 hour. While still plugged in after that time, hold the sleep/wake and home buttons together until you see the Apple logo and then release. This could take upwards of 30 seconds of holding. If this does not work, then you may have damaged the battery beyond repair and would need to make a Genius Bar appointment to have the device looked at for service.