2011 Kia Optima sx won't start

I have a 2011 Kia Optima sx. A few weeks ago I
accelerated to go around someone and my car cut off. A
few times it woukdnt start but if you leave it a few minutes
to a few hours it starts as if nothing ever happened. This
time however it wouldn't start, I've have a new starter put
on and it still won't start. The shop I have it at is saying it
may be a issue with the motor but the car is in great
condition. The alternator was replaced about 3 years ago.
When I get in my vehicle everything comes on fine but it
wont say anything. The break is also harder to press as
well. I dont want to get a new motor if it's not needed. I
have about 197,000 miles on it.