If the battery is old it could still be an issue. Assuming the car has fuel in it and the fuel filter is OK, is there any reason for you to think you aren't getting spark? Have you done any work lately or anything?
When the car does start, does it run well? Does it ever hickup or lurch when running and driving around? If not, I'd not suspect the fuel filter too much.
Here's how to check out a starter solenoid but be cautious, the currents involved are high and everything's hot under there too:
Diagnosing A No Start Situation