2012 Hyundai Santa Fe not starting/hesitating to start occasionally...

My 2012 Hyundai Santa Fe has about 114,000 miles on it. Occasionally it acts
as though it isn't going to start. The noise it makes when it acts up is hard to
describe. It isn't a clicking sound that would indicate a battery issue. It will
hesitate and you can hear what sounds like the starter running and will
eventually turn over. When it does eventually start, you can shift gears and all
the electrical works (radio, heat, etc.), but the engine still doesn't sound like it
is fully engaged. The thing that makes this even more weird is that two dash
lights come on and won't go off when it hesitates to start. It's the traction
control light and the hill descent light. I can usually remedy the problem by
turning my car off and starting it again. The second start is usually a normal
start. The car continues to run fine once started. I have taken it to a mechanic
and the dealership multiple times. The only solution that the dealership
suggested was replacing the started, which I did, but that clearly wasn't the
issue as it continues to do it.

Anyone else have this problem?