The clicking sound you heard was probably the solenoid.
Although your battery may seem strong, it doesn't mean that it is; the only way to know is to have it tested at an autopart store.
I don't think your problem is the fuel filter or fuel pump; check your battery cables for corrosion and make sure they're not loose at the battery/solenoid/starter. Also check your ignition switch; if it's loose it could result in your car turning off.
If you have a digital voltmeter and feel confident about doing more in depth tests, let me know and we can do more troubleshooting. If not, have a mechanic to look at the starting system
Tuesday, December 2nd, 2008 AT 12:53 PM