1....First in this case I'd charge battery, if you have a maintainer, give it a charge with a "regular" charger, then use the maintainer for at least a day indicating it is "full" charged. DO THIS with at least one cable unhooked from the car, or out of the car
2...If you have an accessible battery and a hydrometer, check the cells for gravity, and "equal" between cells. If not, take it somewhere and have it tested. If it comes back "bad" I would get "a second opinion." In this case, as you described, the battery may well be "bad" such as 1 dead cell
3...AFTER you do 1, 2 above, put back in the car run it and warm it up. Check battery charging voltage, right at the battery with a good meter. give the engine some RPM to simulate "low to medium cruise" IE 35--40MPH. Exact not important. If it runs near 14 (warm should be 13.8--14.2) double check by turning on loads, headlights, heater blower, AC, whatever you have. It should be at least 13.5, the closer to 14 the better.
If you have a known good spare battery, you can temporarily bypass 1 and 2 and perform step 3 using your spare battery. Make sure, however, that it is "up."
4...If "3" is OK, measure "running" coil + voltage right at the coil. This will vary, but if you are using a factory type ECU setup and you should be running a ballast, this will run from 9--10 on up to maybe 12V with the battery at 14V. If you are running a heavier coil, follow manufacturer's instructions CAREFULLY. Some of the Accel and old Mallory coils actually used TWO ballasts in SERIES