My 97 GTX does not beep when attaching the lanyard. Cranks up and run's fine. When I pushed the start button 5 times, the display said "Hi Temp Sensor" I may be asking the obvious but is this the Hi Temp sensor ?
If it does not beep but still starts up then your buzzer needs to be replaced. Yes replace the sensor.
You could go here to get a replacement; http://www.seadoowarehouse.com/