Please help! Single click no start. Even with a new starter

I have a 2008 Dodge Charger 2.7. Here’s the problem. When I first get in my
car, it will start right up. But after driving it for awhile and I turn it off, it will
make a single click sound when I try to start it again. I’d try to start it several
times and each time it makes the single click sound. After a few minutes
(sometimes longer), the car will start again. But if I turn it right off and try to
start it again, it does the same thing. I replaced the starter but it is still making
the single click sound after I have driven it and turn it off and try to turn it
back on. I took it to a mechanic and he used some type of relay that has an
on/off switch to bypass something to crank and start the car. (So the relay
that was in the fuse box was removed because of the single click sound and
replaced with the relay with the on/off switch. When he flipped the switch to
the on position, he said he bypassed something and the car did not make the
single click sound but actually cranked and started up). He mentioned
something about the intergrated power module. Can someone please help
me?