Could coolant drip from tank onto starter and cause a short circuit? When the key is turn to try to start the car, starter does not engage. Just get a clicking sound. Battery is brand new and fully charged.

 

As always, double check the battery, just cos it's brand new don't assume it's charged.

Check the pats light on dash to make sure the immobiliser is turning off. (light should go out no flashes)

Make sure it's in Park also try neutral.

If you have the zf gearbox check the 2 bolts on the side.

Check the battery earth strap

if it still won't start remove starter and see if direct power will spin it, if it does put back in and see if it starts, a few people have done this and it's worked fine after.

 

And don't forget to fix the coolant leak while you're at it!

 

Well think about that for a minute?

What happens when you are driving in the rain? The starter and it's cables are exposed to the elements so a little coolant won't cause anything to short out.

If the battery is good like the others advised. I would make and break the electrical connections because corrosion builds over time and it's always good to clean up any high current connections.

If no change then remove the starter and get it bench tested. Starters last a long time but do fail.
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Is there a neutral lock out switch on the transmission? It won't turn over in neutral either.

 

Not on the trans.

+1 on post #4.

 

But is there a lockout switch somewhere or a relay/ fuse that could be preventing a complete circut to the starter?

 

If the gear selector is not in p or n it will not turn over, also if the alarm/immobiliser is not deactivated it will not turn over.

Also check all fuses, including main fuse in boot

Check, as best you can, all wiring to make sure the is no obvious fault there.

 

Get JTIS and use it - it's free on here. Has all you ask and more.

 

Check voltage to the starter - the starter itself could have crapped out.