2004 Saturn L300 Saturn L300 semi-frequent car starting tro

Engine Performance problem
2004 Saturn L300 6 cyl Automatic 99000 miles

Periodically my Saturn L300 will not turn over on the first start. It happens about once or twice a week-- in order to get it to start, I usually have to wait a few minutes, then I have to depress the gas pedal while I start it. After it usually starts fine, the check engine light comes on, and at the time of this writing the car does not stall out while driving; the problem disappears for about a week afterward too, the car starts fine the next attempt from a cold start and the check engine light is not on either.

Tried replacing the old battery, still same problem.
Thinking something with the fuel delivery/filter/pump?
Please help! Thanks!