I've got a 97 challenger, runs good, have had it out a few times since buying it a couple weeks ago. I read a few posts about DESS, mine has never made a sound.
This is the only issue that aggravates me about the DESS, waiting for the two beeps to start the engines otherwise you push the start button and nothing happens...
...same issue or different?
Dr Honda has a buzzer replacing thread, I'm going that route next and it sounds like you may benefit from that too. 10 dollar parts...cheap fix.