My radio stays on when I shut off the car and it's draining my battery. Now the battery is total drained and won't charge with a jump.

I suspect parasitic draw. All vehicles draw some power from the batteries when the car is shut off. Certain accessories such as clocks, radios remote door openers and alarms always need power. The normal power used is called parasitic draw.

It is always a very low draw so it doesn't run the battery down. If you install accessories like shortwave radios or plug things like inverters and portable refrigerators into the accessory socket and operate them too long without the engine running you can drain your batteries to the point where the engine won't start. If there is an electrical short in the vehicle or a malfunctioning accessory it could be drawing much more than its normal load causing a drain on the batteries. If you leave your door open and the inside lights stay on all night you could drain the battery down till the car won't start.

Here's also a good resource for your car specifically on narrowing down the cause of the drain.

You need to charge your battery up more. Either get a battery charger or leave the jumper cables hooked up for a longer period of time.
Your battery was probably completely dead. You might even need a new battery...they really don't like to be completely drained.

Your battery is not fully charged and may not be accepting a full charge. Remove your battery and put it on a charger overnight. Take the battery to a parts store and have them hook it up. They will then be able to tell if it is taking a full charge or not. If this is a new battery it will take a full charge but it is still getting drained by something such as a radio not shutting off automatically, if you have that option.

If it runs you have one of 2 issues. 1. The battery is bad and the alternator isn't able to keep it charged (you will have to jump start it every time the motor is shut off). 2. Your alternator is bad and the battery is running the car (when battery is drained car will stop running) which is my belief as the battery light only comes on when the alternator isnt charging. Have the charging system tested at your local AutoZone/Advanced Auto parts store they normally do it for free.

Check for a battery drain in the vehicles fuse box circuit.

First have your battery load tested, and your alternator checked for proper charging amperage. If that is ok then you have what is called a parasitic drain that is draining your battery overnight. A parasitic drain test will need to be ran and repairs made.

Good luck. i hope this helps.

Thanks for choosing FixYa and welcome. Trunk lights can be tricky. Make sure it is not on. Check for any lights in the glovebox or under the hood, dome lights, even the radio. If your battery is draining, check the wires, battery post, and terminals. They may need cleaned. May need a new battery if it continues to not hold a charge.

When a battery is very low, even a jump won't work because the battery takes too much out of the jump. Take the battery out and have it charged up.
If it won't take a charge, get a new one.
But also make sure the battery terminals and cable ends are shiny and greased.

If you really want to be sure, put a voltmeter on it.
A good battery should be 12.5.
When you crank it should go down to about 10.
If it goes below 9, either the battery is too low, or the starter is draining too much.
If it never goes below 11, it is not draining enough, and the solenoid is probably bad.
If when you stop cranking, it comes back up to over 11, then the battery is good, so the starter is probably bad.

As long as it goes off when you switch off the engine, it won`t drain the battery. If it stays on, it means it it is connected directly from the battery and yes.. it will drain it.