There are only 2 things that have rotating parts in your computer that can possibly make clicking noises.

1. The Hard Drive
2. The Fans

If your computer still boots up, then there's no way it's your hard drive.  Odds are when your internal fan begins to speed up it's nicking on a cable somewhere in the laptop causing a "click" sound.  This can be completely intermittent and random… also annoying.  I would guess it's the exhaust fan blowing air out of the laptop.  Perhaps put your hand on where the air is blown out and see if it stops blowing air after the click or put your ear where the air is blowing out and see if it gets really loud.  If not, then it could be the processor fan is catching on something… which would not be good. 

Either way it should be a completely fixable problem if you can get into your laptop… feeling brave?