How to disable the factory car alarm on my Honda Passport?

It's a 1998 and I got in it to start it today and it wouldn't start. The alarm went off at first, the sound is dead in it so it's just the lights that blink and you can hear the clicking sound, but the horn doesn't go off. I turned off the alarm and tried to start it again, nothing. I opened the door and closed it again, I tried starting it with the door open. I tried letting it sit for a few minutes. I tried locking and unlocking it, using both the key and the keyless entry. I realized the battery was bad so I got a new one, it still won't start. Everything is clicking like it should but it won't even try to turn over. I put the key in and try to start it but I hear no engine, just a slight very quiet clicking.

Is the alarm dead? I took out the fuse for the anti-theft but it didn't get the car to start.

Your post is some how confusing me a little: Which battery you've replaced: The car or the remote? What the remote look like?

Normally, after closing all doors and putting the key in the drivers side door lock, turning to the left, then to the right all the way will unlock and disarm/reset the OEM alarm system and you've done that.

Your description of the system is after market because if it's OEM, only the car's own horn honking, if it's a siren and flashing lights, it's after market. Try this if lock/unlock with a key did not work:

To start with, you can identify which after market system you have by using the FCC. ID.# found on the back of each remote. This site will help to find out the system the car has: http://www.remotesandkeys.com
Inside the vehicle in the driver side under dash, there should be a valet/over ride button, it's a hidden device-switch, a little spring loaded micro button, red or black possibly and is probably down under
the dash area, near your knee bolster. Older systems will have a flip type toggle switch. Locate the button or switch, turn on the ignition key, press and hold the button until the alarm chirps one time, for toggle types, key on, flip switch in the opposite direction, then key off.

This should over ride the system, and only the key-less entry part, if installed, would still be operating. You would get a single chirp to confirm from the siren. The LED (Light Emitting Diode) light in the dash
should also go on solid. This indicate the valet/over ride has reset and should correct any issues like starter disable. The key-less entry, if installed, will still be operable. Then have the system inspected for the alarm issues you are experience at a local shop.

You would repeat the same steps to toggle back into user mode. That should do it for 90% of the after market alarms system.

Look at this link if you want to remove the system:
http://www.d-series.org/forums/audio-electronics/150187-removed-car-alarm-car-wont-start.html

Hope it help and good luck to you. HTH

Edit: This site could be helpful: http://www.the12volt.com/

You said you " realized the battery was bad so I got a new one, it still won't start".
The remote battery or car battery?
But either way, make sure BOTH the remote & the car battery are not the problem.
If it was the remote battery you replaced, the car battery may also be the problem.
The starter in an automobile needs much more amperage than all the other systems combined, so a car battery will run the radio and the lights and still not be able to start.
So, after making sure the remote battery is good, then if you have a trusty neighbor with jumper cables or AAA, then call & ask for a jump start.

Also, don't forget. Whether using the key with the door or the ignition
The door must be still be CLOSED, when deactivating the alarm.

SIMPLY PULLING THE FUSE SHOULD KILL THE ALARM AND MAKE THE VEHICLE START AS NORMAL, PROVIDED THAT IS THE ISSUE.

I had a very vague understanding of algebra at school today.