What was the battery level when it switched off?
If the battery has completely drained, it can lead to the device not having enough power to even show the charging graphics on screen.
When this happens, you need to leave the device plugged in for anywhere from 5 minutes to a couple of hours in order that the battery can charge up to a level where it can safely power the device, at which point the screen should come on with the usual charging indicator.
This usually tends to only happen after a prolonged period of non-use, so it probably doesn't apply in your case, but it doesn't hurt to try in your case.