Replacement of battery connector

Hie my name is Chuck and am from South africa,i have a iphone 4s which has battery connectors issue,after damaging when i was replacing the screen,the iphone powers on perfectly but the problem is that after a while 5-10mins of using it,it reboots on its on and works again then again reboots,but when u leave it eg on top of a table it doesnt not even reboot coz i did that when i went to work and left the stop watch on juss to see how long it would be on,when i came back it had been on for 6hrs,without rebooting.

And when i put it on charger it shows that its charging but the battery percentage doesnt go up its keeps still on 13%..but when u leave it on the charge for 30mins or so and reboot it,the battery percentage would have gone up to maybe 35%..i cant see the battery percentage recharging or discharging..what could be the problem?

Hope you guys can help