iPhone 4 will not turn off, and instantly uses battery up

Hello everyone, my name is Fraser and it's a long story, but I got 3 iPhones for free. (2 iPhone 4's and a iPhone 3GS.)

I have a problem with one of the iPhone 4's, what it keeps doing is turning on to the apple logo and then immediately turning off. This then leaves me to turn it on. Only to leave me with the dead battery screen.

Fantastic.

I would also like to note, is while there are no visible markings on the outside, the screen seems to be a little bit strange, in which it has tiny pixel lines vertically.

Is there any way I could fix this?

Thanks!
Fraser