The battery would need to be quite dead to not operate the Arc4. If you put a battery that is close to that point in the Arc4, this is what you would see:
1. Install new battery
2. RFS with top levels truncated (could skip normal RFS altogether). This is your first indicator the battery is dead. (note: if you turned off RFS, you won't see it ever, even if the battery is dead)
3. Turn light on to one of the higher levels.
4. Light switches down a bunch of levels in rapid succession all the way down to level 16. This could create quite a few flashes in the process. Some people interpret this as "the light is punishing me with wild flashing for no reason". This is your second indicator the battery is dead.
5. Settles at level 16 for a bit.
6. If the battery has some life, it will run for 10 minutes or so at level 16. If not, it will start to flash on an off.
7. Finally the light will shut off and not come back on.
8. If you let the battery sit for a bit and then power cycle it, you might be able to get the whole dance once again.
Change the battery.
Peter