Do you know the model name of the car alarm or the model #? Is it the factory Toyota alarm that cherps to the horn "Karr alarm" or the better upgraded genuine Toyota alarm that has a fancy cherp "tweet tweet" sound just like a lexus??? Is it functional at all (if equipped with keyless entry, blinking lights, cherping sounds/beeps) what is happening?
You can try this...
Since you do have a signal blinking at your l.e.d. indicator try holding the button behind the blinking l.e.d. indicator for 5-10 seconds. Once the light is steady it should be disarmed (try your remote again check what's going on is the horn sounding/siren working, lights blinking, doors locking/unlocking???). Push it again for another 5-10 seconds to re-activate it (Are all the functions work as normal???). Try it a couple times until if starts functioning again. Make sure you do this while all the doors, trunk are locked. Test with the remote.
I forget but their are different settings you can set it to and sometimes will also depend on how you longer you hold the remote button. This happens to basic alarms most of the time where the lights, horn, cherp, locking system one or the other sometimes goes out.
Try it out if theirs no hope reset the battery for couple minutes locate the main unit "box shape" unplug all the connectors for 1-5mins and plug all back in. Do the same thing and if nothing happens have Toyota re-program it.
Sometimes the memory gets erase after a couple hours Toyota may have to put the code back in so your system will work again and function with your remote as well.