When I try to reconnect my battery it starts without
the keys being in the ignition. What could be
Does it have remote start?
Stuck starter solenoid is the most common, requiring replacement of the starter as it is part of the starter assembly, the other problem could be a cross circuited ignition switch or wiring, sometimes a light tap on the starter will dislodge the solenoid but it will happen again so it is not a fix.
Search Hyundai Santa Fe Questions
Hyundai Santa Fe Experts