That doesn't sound like anti-theft mode, which works normally in two ways, 1. you get no spark, so the engine doesn't start at all, or 2, the vehicle starts and cuts out 20 feet way.
It sounds like you are in Limp Mode, and that signifies an issue that the ECM (engine computer module) deems serious if you go over 10 mph. It is just enough to get you to a garage to fix the issue. Is your Check Engine Light on?
You need a local auto electrician with a professional grade scan tool computer to diagnose the issue. It is probably a failing sensor. With an issue like yours, you can't GUESS what is wrong as there are so many parts involved that could cause it. But Limp Mode is only for VERY serious faults.
https://www.google.com/search?q=mobile+auto+electrician+near+me
Limp Mode
https://www.google.com/search?q=2003+Hyundai+Tiburon+GT+V6+limp+mode
....
500 is too low for and automatic in drive
normal idle is 850-900 and should not drop below 800 in drive as the ECM should be adjusting for the drive load when in gear
take it in to an accredited service shop that works on your make of vehicle and have the problem diagnosed properly and quote
bosch or NGK mag wires are best.
plugs any you want , if car short miles car, every year go cheap plugs , if hard to reach go best plugs.
I like NGK the best, but there are other good brands.
