Well, the click is either the starter solenoid, or the starter enable relay in the under hood fuse block.....
Was this the reason for the new battery and starter? Or have they been installed for awhile and this has just happened?
If you can feel/hear the starter enable relay click, when someone turns the key to the crank position, and it doesn't crank, see if there is another relay in the fuse block with the same number and swap relays....if it now cranks over, bad relay....
If it still does not crank over, attach a test light to ground.......now touch the red cable where it attaches to the starter....test light should be bright, just like if you touched the positive terminal on the battery with it......if it isn't we have a positive battery cable problem......now go to the yellow wire connection at the starter solenoid....attach your test light....should be off......have someone turn the key to the crank position.....the starter enable relay should click and you should have the same brightness as when attached to the red wire......if yes, bad starter solenoid.......
If no, there is a 30A fuse(F12UA) that feeds the solenoid...see if the fuse is blown, or check with test light that it is getting power......