Ok that verifies it, if the clicking happens THEN the light turns on over the steering wheel, THEN you can start it, its definitely the computer. No doubt about it, since mine did the same thing for 3 months before it finally crapped out completely. Either get it repaired or see if you can find a new one. Dealer charges like $540 for a new one, sometimes you see 'em on ebay for cheap, but it might not work. Personally I didn't mind spending the $187 to get it repaired, escpecially since I knew it would be under warranty after they fixed it :D
I can tell you it ain't a relay. Replaced all of my relays hoping it was just that, but all I did was waste $40 on relays. :\