What i am posting isnt related to your problem, but similar in some ways.
The low battery wouldnt cause this issue. The battery drained from trying to crank the car. Mine did the same, when my fuel pump went out. I checked the battery before trying to crank and it was 12v and then dropped to 11v after a few cranks.
Sounds like your ignition coil is shot. Anything outside the oem ohm spec is considered bad. When i checked my fuel pump, it was at 6.8 ohms, and the oem spec on it was supposed to be between 0.2-3.0 ohms. When i replaced my fuel pump, the reading was 2.0 ohms and the car started
This is from my Lexus IS300
Maybe Samurai or Nick can chime in on this