2003 Denali Won't start fast clicking

So I bought a 2003 Denali XL. 78K miles. Runs great. Drove it back from CA to OR. Drove it all week. Then went out to start it this morning, and all I get is a very fast click click click click. I jump it from my suburban, and it starts fine. Drove it all day, drove it home, turned it off and let it sit there for a few hours, try it again, and I get click click click click click. I checked the terminals, and they look clean. I had this problem with my suburban a few years ago, and the side bolts were mucked up. Cleaned them up, and the problem went away. These bolts look brand new. Connections are tight. I could suspect the starter, but when I jump it from another vehicle, it starts. Should I have a different battery, now that the climate is different? (CA vs. OR). Do I just need to get a battery charger, and trickle charge the battery? Is there some odd fuse linking the battery and the starter?

Welcome to AF.How about testing the battery, basic diagnostics.

Sounds like battery to me. check to see if you need to replace it. Most automotive parts stores will check it for free.

Well, the battery that is in it, is about 3 months old. The previous owner put an AAA battery in it. I've not ever used them, so I can't say good or bad on the quality. Would a place like AutoZone test it for me? Wonder if they're open on New Years Day......