2009 Infiniti g37x won’t start

My car will not start at all or it will slowly turn
over and barely start. I know the problem is
not the alternator because I just got it
replaced by a mechanic who was attempting
to fix the same problem, and my battery is
also pretty new. After I needed to jump it and
drove the car to work I shut it off and turned it
back on to see if it would start and it would so
I think that means it is still charging so
something might be draining the battery while
it sits? I have also noticed some glitchy
electronical problems which might help
diagnose my problem with starting the car. All
of a sudden now when I lock my car it doesn’t
make the beeping sound but it does lock.
After I got a new alternator the back windows
wouldn’t automatically roll up but now they
are. Also, I always shut the A/C and radio off
before I shut the car off, and sometimes the
radio automatically turns on when I turn my
car on. Hopefully this will help with the
diagnosis. Thanks.