Iphone only turns on when plugged in?

Hi, I dropped my iphone 3gs (ios 6.1.6, jailbroken). Since it turned on twice but never went passed the apple logo, then I tried plugging it in to the wall, and it turned on once and went to the home screen and was fully functionnal, but as I unplugged it it went straight back off. I have tried plugging it into Itunes, at first it doesn't recognize it, but if I put it into DFU mode it recognizes an Iphone in recovery mode. I have also tried restoring many times (with ireb, with a custom firmware from snowbreeze) but everytime I get different errors (1602, 3194.). Now, when I plug it into the wall it seems to be in a boot loop, it doesn't go to the home screen, and everytime I look it is either on the apple logo, or black and is turning back on again. And still turns straight off when I unplug from wall.
Please, any help would be much appreciated. I'm dying to use my phone!

Sounds like your going to need to replace the battery. This is a common thing lithium ion batteries do.

I would say that the battery has dropped a cell, most phone repair shops can replace it but read the contract they make you sine. I know of one person that signed the contract and it said they had 48 hours to pick up the phone or they would keep it.

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