I store my vehicle in the winter in a warm garage. I start it once a week , run it, then let her sleep. A few weeks ago, I went through my routine and all was well. A week later, I went out and nothing but heavy clicking. Checked the battery and found 2.2V, so replaced it with new. Currently 12.2V. Car won't even click. Checked starter relay fuse in passenger side kickplate. It's a 10A fuse and is in good condition. Swapped out starter relay for another in the relay box, and still nothing. Pleeeeease..........anyone got any ideas? The clicking before battery change signaled to me that the starter was ok and solenoid was trying to engage, so I'm truly at a loss.

Double check your work to see that one of the grounds around the battery were not accidentally disconnected.

Check the neutral safety switches. If this is an automatic, confirm the selector is in park. If manual, confirm shifter is in neutral and clutch fully depressed.

why are u starting it every week?

Good advice.

Also, you may want to invest in a battery charger. These cars are notorious for draining batteries if they're left idle for a week or longer.

Or at least a battery guard to keep it topped up when the car's sitting idle for a few days.

Raise the car up and check for loose connection at starter signal wire. Have someone help you. Get a volt meter and set meter 20v DC. Remove signal wire(will be smallest gauge wire to starter solenoid)and hook positive lead to the end of connector(unplug signal wire from solenoid for testing)and negative lead to good ground sorce. Have your help to crank key over all the way in the start position and watch volt meter to verify good voltage signal. If no signal is present then check all fuses in out of vehicle. 2 to 3 fuses can cause no signal to starter Ignition fuses. Check all connection to battery ground and power. If you do get a signal voltage to starter(should be 12v to 10v)then plug back wire. Grab a hammer and have your help hold key all the way over and hold it why you strike the bottom of starter. If it kicks over you have a bad starter. Your car sits and the brushes in the starter will start to stick over time. Hope this helps!!

would the "PATS" system need to be reset if the power has been disconnected? jw.

This thread makes me wonder if the problem is actually related to the storage and periodic starting of the car, or whether it was just a random happening.

Personally, I do NOT start my car every week when I winter store it. I put it on a battery tender, then start and run it once a month till it is fully warmed up. (Fresh oil and filter and full tank of gas before putting it away). So far, I've had good luck.

Having said that, you've replaced the battery, relay fuse is ok, relay is new, so time to go under the car, and check out the starter and wiring connections. Sooner or later, this problem will get solved. Good luck.

When key is in "ON" position, do you have power inside vehicle? Dash lights, radio etc?

No it would not. If this was the case, the car would crank but not turn.