Might be something wrong with the alternator. Also you need to double check the wires around the battery and starter. Some of them can be loosen. It can cause a lot of troubles. Just make sure that all wires were tighten properly.
battery needs replacing, make sure you replace it with a battery of correct cranking amps
The 1996 Toyota Camry starter is located near the front of the engine, at the bottom. You can follow the positive battery cable from the battery to the starter.
Follow the + battery cable should connect to the starter solenoid (relay)
maybe on the top of the starter Follow the+ battery cable should connect to solenoid
Because it has to be replaced.
Solenoid or battery *Check the alternator as well. When my Camry did that, the battery and alternator both needed replacement. -andey78
It is necessary to disconnect the battery to safely install a starter. When the battery is disconnected the radio loses its presets due to no power going to it.
Remove the battery and the cruise control actuator. The starter has two bolts holding it in. Remove the bolts and wiring, then install the new starter. Re-install the cruise control and battery.
Look at the lower end of the engine - try to follow the + battery cable
Possibly bad spark plug cable(s) (have you replaced them since 1996?)
Where is the starter on Toyota Camry 1995
remove neg. battery cable disconnect both electrical wires to starter solenoid. remove 2 14mm bolts that secure starter to transmission and remove starter