The only way it could be the battery would be if the battery voltage was below 10.5 volts or so. You can check that with a meter, and if you don't have a meter, get one.
But if you can crank the motor over with the battery, I'd be surprised if it's below 10.5v.
Start trouble shooting crank no start. You can unplug the cam sensor, then try and start it, key on, crank, key off, key on crank, key off, key on, crank, key off. Do that up to 6 times and if it doesn't start, it's not the cam sensor. If it does start, it's the cam sensor , wiring, or position of the cam sensor.
Are you sure the crank didn't move even a little, maybe when pulling or installing the balancer?
If it doesn't start after tests, recharge the battery and inspect the crank sensor.