When I turn the key to start, some thing trips and everything goes dead like the battery is dead or some thing. Then there's a clicking sound that comes from somewhere under the dash board (closer to the passenger side).

I go to the engine bay, disconnect and reconnect the battery then everything comes back to life. I try to start and it'll start (some times. usually takes a few times).

I've changed battery, battery terminals and the starter. I've also inspected the battery cables and they look fine. Should I replace them anyway? What's the clicking sound about? Is it a fuse? flasher? solenoid?
This happens only sometimes. And it's always at the worst times. Like when I need to get to work or stop at the pump and try to leave.

 

The clicking sound that you hear may be the starter solenoid. It located in the lower right side of the engine. With a new starter, it may not be the starter itself but maybe a lack of electrical power. Check your starter relay to see if it is good.

It is best to do some testing rather than throw parts at it. It can get expensive and not fix things.

 

Tighten your battery terminals and check the ground cable on the engine.