My car has never had any trouble starting. I came out of work yesterday where it was very cold and I put my key in my ignition and then pushed in the clutch fully and turned the key. All the electrical stuff like radio, dash, and lights all work, but the car wouldn't even try to turn over. I heard a light humming noise but nothing else. I pumped the clutch a few times and then tried again and it started up fine. But when I got home it would not start up again. The battery is fine, provides power to everything so I think it's the starter. But someone told me they think it is the solenoid, but I don't know what the difference is. How do I know what it is? My car is a 1997 Honda civic LX 5 speed.

Remove and fully charge/replace the battery. Most auto parts stores will test and charge batteries for free. My bet is that the battery is toast.