standign voltage shoudl be 12.6V, charging/running 13.5 to 14.5. Voltage naturally drops during engine crank, but the electronics are designed for that and even calibrate injector pulses for the lower voltage. I really doubt the battery has anything to do with it. For a quick check, hook a battery charger with a start mode to it while cranking or jumper to another vehicle if you can. P0700 is a generic trans code meanign the trans has a code set. Tranny shop or dealer or sometone should scan it. Maybe you can buy or rent or borrow a scanner for the TCM at an auto parts store.

My car threw a few P07xx numbers and it was just the solenoid pack (common problem by that age) but could also be stickly/slow valve body and speed sensors. None of which require a full rebuild or even a big bill.