Everything good now?

 

Hope so, still need to pick up and replace the battery. Recovering from 4 broken ribs a week ago, so I'm not up for leaning over the trunk to replace it yet.

 

You take care of yourself! That battery can wait.

 

Update: replaced the battery over 10 days ago and this morning the alarm started up again. Put the window down and the key in the ignition to stop it, and then it started honking again! Again, this was while it was in the garage and unlocked for over a day and a half. I'm going to try just not locking it or using the remote for a couple days to see if that makes a difference

 

It is plausible that new battery isn’t fully charged, or possibly failed.

 

Do you leave any devices plugged into the power outlerts?

 

Now I'm getting confused. My "new" battery is reading 12.5v (direct on poles with the engine off) and my old battery, which I haven't returned for the core charge yet, is reading 12.6v. This is crosschecked with both a voltmeter and a trickle charger. I don't leave anything plugged in to the power port including the lighter. Could the battery read a little low after having the key turned to acc for an hour?

 

Yes, it could, sounds like you may have gotten a bad battery , should be 12.6 to 13.2 volts

 

I think I was using the wrong selection on my voltmeter. I was using the 12v battery selection, but I think I'm supposed to use the DC selection for a car battery? Using the DC selection, I now show 13.0v for the new battery and still 12.6 for the old. I then tested it running to see about charging output and got 14.5v. A couple hours before the tests I had removed the remote from the key and wrapped it in foil. Since then I have been able to remove the key without the alarm triggering. I'm now leaning towards some type of remote issue, but I will keep it sealed and away from the car for the next couple weeks to test.

 

What does "removed the remote from the key" mean? By "remote issue" do you mean fob? Are we talking about an HHR?
If that was meant to be "key ring" then your answers to the earlier questions are suspect. (stuck panic button, something accidentally pushing buttons etc) Seems the panic button is stuck, the contacts are shorting at least.
Yes, leaving the key in acc will drain the battery.
I don't know what the difference could be between "12V battery" and "DC". Never seen such a thing. Maybe read the manual that came with the voltmeter