iPhone only working when plugged into charger. whats wrong with it?

my iPhone 4 is acting weird. Ive had it for about a year and a half and lately if i would drop it (less than 1 foot) or even set it down ge it would shut off and not turn on. i would smack it and tried to turn it on and it worked. the other day i dropped it and the whole screen cracked:( the screen can be fixed easily but what i don't understand is that my iPhone will only turn on when it is plugged into my charger. if i take it out it instantly turns off. any idea?

also, The battery percentage does not increase while plugged into the charger