Check for voltage between battery and starter. You need approx. 13and a half volts to start a car. Battery cable should be carrying 12 at least. Check Negative cable for continuity. If this all checks out and engine jerks when starting make sure timing belt hasn't stretched or that fuel pump pressure is adequate. Long distance diagnosis is difficult without hearing the problem
You probably have a bad ground. Check the grounds on the brake lights.
The computer only resets when the battery is removed. The alternator just charges the battery, so if the battery is left connected when the alternator is replaced, the computer should not reset.
The battery needs to be replaced
Battery light usually means alternator not charging. Most common solutions would be be a bad alternator, bad connection, or loose alt belt.
did you check the alternator??
Inside the alternator
The battery in the remote needs to be replaced.
Voltage regulator or loose wire.
Check the battery cables or starter.
Alternator is not charging. Have it tested and/or replaced.
You can have the alternator tested free of charge at just about any major auto parts store. By the way, a bad alternator will not "discharge" a battery - the alternator's function is to provide the charge to the battery. If the alternator is faulty, then it is not providing the charge necessary to keep other components from discharging the battery. I had the alternator tested and it was charging. If the alternator has a bad diode, it will discharge the battery. I replaced the alternator and everything is fine.
It could be an alternator. Check with a mechanic if that is the issue.