Hyundai Repair: 2001 Elantra Keyless Entry, turn signals, keyless entry

Question
My Keyless entry/alarm stopped working over a year ago.  When I first asked them to check it out during a routine oil change, the dealership said that it would cost in the hundreds to have fixed, because it would take a lot of time to check every possibly wire connection.

I just wanted to check how accurate this is.  Any help would be appreciated.

Answer
To have made that statement, I'd hope that they had already checked the simple things, like whether the power locks work whether the remotes are still functioning.  

If there's an actual electrical issue in the wiring, it's true that this will likely take a significant amount of time to sort out where the issue is.  But if the issue is in the remote, a relay, a lock actuator, or the time and alarm control module, I'd think that they would be able to come to this conclusion reasonably quickly.  

There are a few things you can tell me that will help me know what may be the issue with your keyless entry:
1.  Do the LEDs on the remotes light up or flash when either button is depressed?
2.  Do your power locks work normally (other than the keyless feature)?
3.  Do your turn signals flash when you attempt to unlock the vehicle with the remote?
4.  Tell me anything else specific to your concern that you think may be relevant.