My iPhone wont turn on, unless its connected to charger.

have the biggest problem. Just yesterdamy phone was working fine. i began to charge it off a cheap charger my boyfriend just brought me and my phone isnt working at all.. I tried to turn it back on and it wouldn't. This happened previously and I used the sleep/wake and home button method. It worked. NOW it has no effect. I think the battery connector might have been somehow disconnected or something with the battery.

THIS IS CRUCIAL

When i plug the phone into the wall, it takes about a minute or two to start up. (Stays on apple logo) It starts up and its fine. BUT I have to connect it to itunes. I cant disconnect it because it will shut off instantly.

When i plug into the USB PORT OF MY COMPUTER, the phone does the same thing as the wall, EXCEPT it just flashes the apple logo and continues that for just about eternity. I NEED HELP. I figured id ask here because the closest apple store is an hour away. I have it jailbroken, and it is untethered 5.1.1 -