You know, Apple do things in very confusing ways. [br]
If it is anything older than a series 4(i think), the new iOS system and the updated watch app would not pair it and say it's too old. It might just try to unpair all of a sudden, or sometimes the app updates and identifies the watch as "too old"for it and attempt to unpair, but leaves the watch paired even though it doesn't show up in the app. this basically leaves the watch like any other sport watch because all you can do on it is check your heart rate and your activity ring. I mean, Apple Watches are for checking messages and doing stuff without your phone, right?[br]
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About the battery though. When you have problems connecting the battery cables, you probably should have stopped and see whether anything is wrong with the press connectors or whatever they're called. The batteries draining so fast is probably because of poor connection, which might cause overheating. I would advise you to check the connectors again, since it's best to be sure. The old swollen battery might have tugged on the connectors and caused them to malfunction.