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You may have already done this, but it's worth mentioning because a number of people get wrapped up in their troubles that sometimes it is just overlooked- when you purchase a new battery and/or cables, take a terminal cleaner and clean your posts and cable terminals. Just because they are all new or "look" clean doesn't mean that they are going to make a good contact.
Sounds as if this needs to be done by what you are describing- does not start from its own battery but starts fine when jumped.
When it comes to electricity, never assume anything. People get killed by assuming. Sure 12V may not kill you, but if you prove your assumptions, you won't have to worry about chasing ghosts or rabbits.
Thanks. I'm going to work on it more today. To respond to some of the replies I got:
I hadn't thought about the fact that the 2 batteries are additive in amperage being in series, vice parallel. The books recommened around 550 - 850 cca.
As far as the grounds are concerned, everything is grounded to the block, and the block is grounded to the firewall.