Thats the solenoid on the started motor making the clicking,it usually does that when the battery is nearly flat,the alternator and/or battery may be goosed.
Try jump starting from another car.
If you have got or can borrow a multimeter,measure the battery voltage,anything above about 11v 'should be ok',with the engine running it should be about 14.2v,if when running the voltage is low or doesnt change from when not running,or if the voltage is way over(e.g.18v)the alternator is buggered,easy to change,get one from the scrapyard.
If the battery is more than a few years old its a good idea to change that anyway.
Maybe the jump leads aren't too healthy. I've been handed a few dodgy sets before now where the starter/solenoid just clicks and then the terminals start smoking. Either try another set of jump leads, charge the battery on a battery charger, or try another battery and see what happens