The back up lights dont go on and the trunk dont open by the button and the fusis good and lights not burned out

Not to be smart, but have you tried the key? You said you have a box in the trunk, it could be that you have upward pressure on the trunk lid jamming the latch, Have someone push down on the trunk and then hit the buttons to open it, I hope that will work for you

check the fuses could very well be that .......good luck.

i had this same problem. there is a little box (i believe yellow or black)that is inside the trunk.when you open your trunk,pull out the cover on the left side of your trunk.there by the quarter panel and towards the rear shock you will see the little box with a plug attched to it.take it out and open it up.look at the little circuitboard that is in it and if it looks burned,then that is what needs to be replaced.if you already changed the brake switch and the fuse then i am 90% sure that is your problem with the brake lights.i fixed mines and countless other camrys by replacing this box. hope this info helps.take care and good luck, manny

Try unlocking trunk with emergency key,inside remote

Sounds like you may have blown a fuse while installing the audio system.One way to check is to
cross the two wires out of the switch, if the trunk opens, the button is bad. If it won't open check the fuse.The proper way to test the button for power is
with a 12v test light. That said, hope this helps.
Good luck.

I would have to agree it's an electrical problem. It might simply be a defective trunk lid latch switch. Here's the wiring diagram:

wiring shortage. take it to the good electician mechanic.

Does pushing the trunk release button make the back up lights illuminate? Has the car been serviced or wrecked before this problem? Have you been golfing and put clubs in the huge trunk. Either the ground wire for the trunk lid devices is bad or the trunk release wire (purple/orange) and the reverse lamps wire (purple/white) have been reversed.

If you are still looking for the resolution, it's really pretty simple. It is highly recommended that you remove one light assembly at a time, thus allowing you to have a good guide when repositioning the assembly back on the vehicle body. Yes, the only way to get to the burned out bulb in the taillight is to remove the whole darn thing! The bulb burns out every 4-5 months, so I have become good at it...Here goes:

1. Open trunk. Look for small (3" diameter) cutouts in the fabric panel in the trunk liner. They are identical and appear next to the taillight assemblies, on the side, not behind the taillight.
2. Gently use a flat blade screwdriver and pry them open. These cutouts are attached to the inner trunk liner fabric, so be gentle.
3. Notice the phillips head screw inside the opening. Unscrew it slowly, making sure it doesn't drop between the chassis and the trunk liner. Remove the screw.
4. Place soft towel on the outside of the car under the taillight assembly, to prevent scratching the car bumper.
5. Gently grab both sides of the taillight assembly from the outside and pull away from the car (rear direction. Be careful not to pull too hard, or the wiring harness behind the assembly may break.
6. You can now access all lamp in the taillight assembly. Change the bulbs as needed. Also, if you can vacuum or clean the dirt on the chassis as well as on the back side of the taillight assembly, you'll feel better later :-)
7. Placing the taillight assembly back in its place is a bit tricky. It seems to go back easily, but the rubber lining nearest to the trunk opening and where the phillips head screw is, must be placed exactly right or water will leak behind the assembly.
8. Screw in the phillips head screw, but don't overtighten it. You will need to open it every 4-5 months to replace another bulb (its an Audi-VW plan to sell more bulbs).
9. Snap the trunk liner caps back in place and voila, you have done it.

I had the same trouble with mine. My husband took a test light and checked to make sure there was power going to the push button. there was power so he climbed threw to the back and popped it from the inside. we found out that the wire in the back was being kinked by the tailgate. so it was shorting out. He just ran a new one and now it works great but still my key dont work lol but atleast the button does. give that a shot i hope it works foru too