Sounds like grounds to me too.

But there is a mysterious single-click no-start problem that plauges some DSMs. I get it on occasion. I have to rapidly turn the key from on to start, repeatedly, and it starts. Give it a shot. If you get it running that way, I'm sorry but you got the illness - if you find a cure please pass it along! I've tried everything!

To answer your question, the starter relay is under the dash to the left of the steering column among some other relays.
I don't think it's your problem though. If the click you are hearing is under the hood, then the starter is getting triggered and the click is the gear engaging the flywheel. For some reason the starter isn't getting enough amps, or it's stuck.