When battery comes to low it turns off and never charges

MALLIK, the first thing I suggest is that you try a different charger. Use an AC charger as well. Change the cable to make sure it is working okay. Clean the dock connector of all lint and debris, check for broken or bend pins. (you did not tell us if iTunes still recognizes your iPhone when you plug it in) If none of that makes a difference, I suggest you change the battery. Use this guide for that. The battery is available right here. If that does not help, replace the dock connector. Use this guide for that, and the part is available right here. If neither one of those makes a difference, you will have to check the logic board for a bad charging fuse as well as a bad charging coil. Hope this helps, good luck.