most likely your battery is bad if it wont hold a charge unless there is a significant parasitic drain i have no clue on what causes the ticking noise
starter part were the wires are.
I don't know what "after battery is off" means, but if it is clicking while trying to start, then most likely the starter/solenoid/relay is bad.
Causes include a weak battery, loose cables, failed starter.
What causes. Clicking. In my left ear only
Then your battery is still not charged. The clicking sound is the solenoid that has a little gear on it that engages with the ring gear of the engine to spin it. There is a certain amount of voltage needed to push that solenoid into the ring gear and your battery isn't putting out enough. You'll need a jump to get started and then need to consider the battery.
If it does it when you turn the key and the engine does not turn over, it is a weak battery or possibly a loose connection on the cables.
Defective battery or something is pulling power from the battery. Check the glove box light, interior lights, trunk light, hood light, brake lights, etc.
I doubt it rust simply by nature, is a slow deterioration and not sudden and accidental, however turn the claim in to be sure.
start back at the battery, are the leads corroded? is there a clicking noise when the starter is engaged but the starter wont turn? are the leads from the battery to the starter in good condition. Usually any sign of a white powder around the battery or a lot of dirt is a sign of needing attention. The clicking could be a starter relay aor the starter itself needing replacement.
battery
Dead battery or the altenator went. If its the altenator it isn't turning over the engine to start running. If it's the battery usually you will see the battery light appear and no electronics working in the car (or sometimes very dim).
I just had this happen- I disconnected the battery to try and reset the ECU, and when I plugged it back the clicking started. Apparently it was the remote door lock- just try unlocking/locking your car a few times and see if that helps.