You replaced the starter relay, and still have the same clicking problem?
When you started it at the shed was it a dry start or did you have a waterhose hooked to it for cooling the exhaust system? Can you sipon a little gas out of the tank into a styrofoam cup and check it?
The click is the sound of the starter relay engaging... when it clicks, it makes contact internally between the 2 poles to which the battery cables (from battery and to starter) are connected. If it clicks bit the starter does not turn the engine over, either the starter isn't receiving power (or enough power) to turn the engine over, or the starter itself may be bad, OR the engine is locked up and cannot be turned over.
If you accidentally got water into the cylinders from the exhaust cooling system, that water would not compress and the engine would be unable to be turned over until the water seeped out of the cyclinder(s) thru the rings and into the crankcase. This happens when someone tries starting the engine on a trailer or in a lift, and turns the water on going to the cooling system BEFORE trying to start the engine... water fills up the exhaust manifold in just a few seconds, then starts pouring into whichever cyclinder has an open exhaust valve. If you let it set for a bit, the water will drain out and into the crankcase.
If you're not getting full power to the starter, either the starter relay is bad or the battery is bad (has volts but no amps) or there is corrosion in one of the main power cables (to the battery terminals, the starter relay, or even possibly the ground connectection on the front of the engine). Check all connections for corrosion (white powder) and clean.
Lastly, it is not impossible that your starter has a dead spot. I've had automotive starters develop dead spots, and it's frustrating as heck! If all else fails then it is probably time to try a new starter itself. Given the cost and trouble of this, I'd make this the last thing on the list of things to try though.
Regards and never fear piping in with your comments or ideas... everyone was a newbie once.
- Michael