Thanks Disconnect about the connector. I don't have a multimeter but will try the toothpick trick
Sorry you're having this trouble, Sue, but I think Disc is right about the connector. I haven't heard of the Center Pin being Crushed, but I have heard of it getting Pushed Up so it doesn't make contact with the Battery, especially if you Tighten it too much (just needs to be Snug). I don't have a Protank, so IDK how fragile that connector might be.
It might also be Dirty... might have some dried, crusty juice on the (+). I fixed an eGo-type Battery by Cleaning it. Since the battery works on other Attys, it's probably not that (+), but I clean everything regularly. If the contacts aren't bent, then maybe the way the Protank connects is different than the way the others connect, so if the Protank Ωs out OK, then maybe then maybe the (+) is Pushed Up, or maybe it's Dirty.
I clean mine with 91% alcohol Isopropyl Alcohol (IA), but I also use Everclear sometimes (it's 95%, and doesn't leave a residue). The higher 91% alc IA is better than the others (more pure and less residue), but please don't use Wintergreen. I moisten a Q-Tip (just damp) and scrub it good (Batteries and tanks), getting Inside as much as I can, and do all the Threads (inside and out). That's gets all kinds of junk. Then I moisten some folded toilet paper (paper towels, tissue, whatever) and clean the Threads. I fold it in 1/2 twice and get into the threads with a finger nail. I wipe it down after with a clean tissue or TP, Dry it good, and that helps a lot. You can do this on the 510 of both the Battery and any Tank/Carto.
I have an Air Compressor that I Blow Dry my things with at a low pressure (even a Carto's Fibrous Material), but especially the 510. This get out spilled juice, too. However, I'd have to say, Don't use Canned Air, because it leaves a Residue. It's really not even good for Computers and Keyboards (IMHO). If you can't Blow Dry it, just let it Dry really good. If you use water to rinse it (like on the tissue, or whatever), try to use Distilled Water, for less Residue. If it's a freshly cleaned Carto, some people use the Atty to Heat it, to Dry it a little faster.
Good Luck with it, and I hope this helps.
PS:
You can get a Multimeter for like $5. It's doesn't have to be a really good one.
I'd do the same thing if I had my cell phone with me. 
