2010 jeep liberty starting issues

Ok my wife has a 2010 jeep liberty.. I'm
mechanically inclined but I'm not a mechanic
before I go further..

Ok so her jeep when you turn the keycranks over
and sounds like it's running but it's not actually
running it's as if it continues in between cranking
over and running even after you let the key alone. I
though maybe the starter went bad or maybe the
wires were rusty so I replaced the starter and I wife
brushed all wires. The problem continues once
again im not a mechanic but I have enough
common sense if someone can point me in right
directing