I HAVE A CAR ALARM FOR MY 4 DOOR HONDA ACCORD IT BEEPS AND LOCKS THE DOORS WHEN I PUSH THE BUTTON BUT WHEN THE DOORS OR TRUNK IS OPEND THE ALARM WONT GO OFF I BELIVE IT IS A VIPER ALARM

stock alarm or after market.?
check all fuses
if ok, read the operators guide on this .
or the FSM.
opr guide lost in glove box.?
http://justgivemethedamnmanual.com/honda/honda-accord-owners-manuals/

quotes:
The security system will not set if the hood, trunk, or any door is not
fully closed. If the system will not set, check the Door Monitor on the
instrument panel (see page 60), to see if the doors and trunk are fully
closed. Since it is not part of the monitor display, manually check the
hood.

we are not talking the immobilizer system option,.

odd, most really honda's, the horn sticks on. that year. 03
at battery swap or dead. and recharged.

there are 3 related systems.
IMMO (cant start engine) immoblizer
keyfob door mag locks.
and security (alarms)
the all work together,
do say what works and does not.?

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?

with a key unlock doors before attempting to open trunk there may be a button to push on the inside of vehicle also unsure on the button part some alarm sytems wont allow you to open trunk with the doors locked

Programming
When
Key added or replaced. System malfunction.
How
Obtain all keys. A maximum of 3 keys can be programmed. Close all doors and boot/tailgate. Switch ignition ON. Repeat procedure below 3 times: Within 4 seconds: Press key lock or unlock button. Within 4 seconds: Switch ignition OFF. Within 4 seconds: Switch ignition ON. Within 4 seconds: Press key lock or unlock button. System should now lock or unlock vehicle. Within 4 seconds: Press key lock or unlock button. Within 10 seconds: Press lock or unlock button of first key. System should now lock or unlock vehicle. Press lock or unlock button of second key. System should now lock or unlock vehicle. Press lock or unlock button of third key. System should now lock or unlock vehicle. Switch ignition OFF. Remove key. Check operation of all programmed keys.
NOTE: If less than 3 keys are to be programmed, remove ignition key after programming last key.

Please Check Near the Driving Seat With boot (rear door) Open Liver.

if you have a valet key, stick it it on the passenger side when unlocking door, so it wont alarm while you open the door hope that helps

Press the passenger side door lock button. if the driver side door unlocks now but wont unlock when you hit the driver side door lock button, it is usually a network communication problem with the B CAN or a faulty Body Control Module.

the key fob remotes need to be reprogramed or have the battery checked... make sure to have all key fob remotes present when reprogramming...

Blown fuse?, check to owners manual for a theft system fuse.

The buttons on the remote do different things.Number I turns the beeping and alarm either on or off. (2 different settings). The number II button Arms and disarms the car. One beep is armed and two is disarmed. Try it out now, You'll understand.