My iphone 3gs turns off by itself and sometimes doesn't turn on

My iphone 3gs sometimes just turns off... The screen would go white for a second and than it shuts off. Sometimes i can just press every button and it won't change anything so i think my phone is broken but than it just comes magicly on. It doesn't matter if is plugged in or not it just happens randomly and usually when it happens once it happens another few times when i turn it back on and after i turn it back on i have to be really carefull because a little hit on the back side and it wpuld turn off again. Also a month or so ago my phone fell and half of the screen is cracked.

I got the phone from y so it was used but i don't think she had any problems with it.

Pleaseee heeelppp!!!!!!!!!!!!!!