Battery Keeps dying, Car thinks doors are still open when closed .

You didn't say what year or sub model

Will be either a door lock motor assembly (the four doors); which has door switch built in, grounds the purple & white wire, or the hood switch, or the tail gate switch. You can test for the grounds or disconnect the following to test by area:

Connector C0428 on the CCU - pin 21 (the four doors), pin 22 (hood), pin 23 (tail door). Automotive door switch are normally open when door is closed and close or short to ground when door is open.

I would test the hood and tail gate first

ANTITHEFT PROBABLY . THE CAR NOW THINKS IT IS BEING STOLEN. CLOSE ALL DOORS AND TRUNK HOOD ETC . LOCK CAR WITH THE REMOTE FOB THEN REENTER AND TRY AGAIN

Wait for the battery to die or try and open the hood and see if you can unhook the battery. This might be hard to do. You have to get under the car or reach through the grill with something like a metal coat hanger and release the hood latch.

Here are the options for disarming a factory alarm while it's going off:

1. Close all doors, trunk and hood. Alarm will stop after preset time.

2. Hit the unlock or lock button on the remote. (One of the 2 works... I just don't remember which.)

3. With all doors, trunk and hood close, insert the key in the driver's door and unlock/lock the doors manually.

Also, is it a factory security system? Is it a honda key fob? or a remote start system perhaps?

You might just need to reset it. Roll the drivers window down and close all the doors. Lock all the doors with the key ) turn the key to lock twice, The electric locks should lock all the doors. wail a few minutes and unlock and open the trunk with the key. relock the truck or just close it. unlock the drivers door with the key, twice. all the doors should unlock, get in and start the car. Now this does'nt always work. If it does'nt we'll make the system think it's running. Close and lock all the doors. open the hood and disconnect the battery, one ccable will be fine. wait a few minutes. Reach in though the open window and turn the key all the way on. Don't open the doors, go around and connect the battery hard so it does'nt jump or skip. Reach thought the window and start the car/ once it's running. turn it off remove the key and unlock the door from the inside and open the door ( as if you were inside.) get in and start the car and everything should be back to normal.

sounds like the alarm was set and when you opened the trunk it activated the alarm system, seems you got no sound though.
you can go to the drivers door, lock the car up even when the trunk open, then unlock it might have to do it several times. this will reset the alarm

press the lock button on the remote then press the remote start button. if this does not work check remote start status using steering wheel buttons

I have a 2003 camry had the same problem. My solution was to raise the drivers door handle then turned the key and then it opened.

If the alarm keeps going off constantly and the remote has no influence on the alarm its most likely a connection problem. A hyundai dealer might be able to fix it but since you can start the car something you might be able to try is....
Check and make sure the remote battery is in the right way. Make sure all of the doors are closed, the trunk is closed, open the hood, connect the battery, close the hood all the way and try to lock and unlock the doors. Hope this works but if not, sorry it didn't work.

larrylisa2: When you refer to reset, do you mean arm the system?
If so, it can be done providing all the doors, the trunk and hood are closed.
Using your key, you can lock the drivers door or passenger's door and it will arm the system. The trunk, all the doors and hood must be closed.
You can also arm the system without the key in the same fashion insuring all the doors, trunk and hood are closed.
To disarm the unit, you can do this from the driver's door, front passenger's door or the trunk lock.
The other option is the remote. There is one other way to shut down the alarm system. Disconnect the negative battery cable, put the ignition key in the run position and reconnect the cable. This will keep the system from arming until the car is locked.
There is no reset procedure other than the ones I have described.