Replacing the battery will help with a depleting battery where the phone constantly dies after little use.
For a phone that blue screens or constantly reboots and doesn't cahnge the percentage of power, this is the power module or charge connector that has become damaged so will need replacing. Wasn't too expensive for a phone shop here (around £35 for dock connector replacement which was diagnosed by Apple, which I found after paying £40 for a battery replacement previously!!!!).
Hope this helps. It has solved my charge, blue screen, rebooting and battery percentage not dropping issues.