Horn wont stop beeping

It is a known issue. Lots of ideas, mine is a to call out an auto-electrician with a pro-grade scan tool computer. When the battery is disconnected, and the key is in the ignition and the doors are closed, the horn shouldn't go off. Make sure you leave the windows open in case it self locks. After that, you need to do a security reset. There are 3 ways here.

https://www.google.com/search?q=1999+dodge+ram+1500+security+reset

https://www.google.com/search?q=1999+Dodge+Ram+1500.+How+to+make+the+horn+stop+going+off+constantly

Is it possible that the panic button is stuck on the Remote?
..

As a short term solution you can disconnect the horn. This will stop the noise and leave your other systems intact. Locate the horn under the hood and find the attached wire and disconnect it. If you have trouble locating the horn have someone beep it for you a follow the sound to it's source.

lock vehicle with either remote or use lock button on door inside car...then goto passenger side door and unlock it with key..this should reset it

The alarm system somehow got activated , this is usually because the battery becomes discharged or disconnected try doing this:
Remove the key from the ignition
disconnect the negative battery terminal
put the key back in and turn to ON
exit the truck and leave door open
reconnect the battery terminal
get in and leave door open, if the alarm horn stays off it should start.

When you disconnected the battery you triggered the secuirty system.

The horn is located behind the bumper cover, behind the grill. There should be a 20 amp horn fuse under hood in fuse box, and the horn relay is up under dash on the right side of instrument panel, unplug one of these, or both and the horn should stop beeping.

This is probably a bad body control module. I had the same thing happen.
The dealer replaced mine and now there are no problems.

some cars have two horns the other may be obscured

the ground side of the circuit has shorted against something somewhere

my horn did the same thing - we disconnected the horn (which in an 02' is behind the passenger side headlight) I'm sure it's wearing out and we need to replace it.