2006 Hyundai Tucson Car - the battery is totally drained & dead so it wouldn't open with the remote opener. Now that we used the key when the car starts to get battery power back the alarm sounds and the remote won't shut it off. We took out the horn fuse but aren't sure if that will prevent the car from starting when it gets more battery

SOURCE: Imobilising car alarm on Hyundai Getz

it may be worth while changing the battery in the remote as it takes more power to send the frequency to disarm than to illuminate the l.e.d.

SOURCE: my 2006 hyundai sonata alarm keeps going off

One word:

Dealer.

Next time just disconnect the battery until you get it towed as this is a warranty item. I'll bet some wondered if this was a prank question like I did, right?

SOURCE: ELANTRA ALARM PROBLEM

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.

SOURCE: 2005 Hyundai Sonota 2.4GL no sound when alarm triggerred.

Mine acts the same way. I found that it doesn't alarm unless you trigger the alarm. Be sure to check that the alarm fires correctly as mine didn't and they covered this under warranty.

SOURCE: The ignition to my Hyundai Tucson is in locked...

check your key see if its not damaged ok also press the break move the steering wheel slowly and move the key as you are moveing the steering wheel