2008 Chevrolet Cobalt trouble starting.

My Cobalt has had trouble starting the last few
years. It first started out by a delayed starting,
starting on the 4th or 5th turnover. It evolved into
not starting on the first try but would always start on
the second attempt. I resolved this about a year ago
by turning the key on to turn the electricity on for a
few seconds before attempting to start. Doing this
resolved my issue until now. I now inevitably have to
try to start the car twice to get it to run, unless I've
used it in the last 20 minutes or so. There are no
unusual sounds, just the sound of a car turning over
until it musters up a weak startup, which sometimes
turns makes it run and sometimes doesn't, if that
makes any sense. When I first had the problem I
took it to a local shop guy I trust personally, and he
diagnosed it as the fuel pump. However after
replacing it and 500 dollars later it made literally no
change. Anybody with some insight to what could
be wrong?