What he said! There is something wrong if you are only getting 3 hours of batter life.
As you stated, when you turn off the phone,
it is off. There are no programs that will run in the background whatsoever, so finding an alarm program that will work when it is off is going to be impossible.
When you install Windows Mobile 6.1 and run KaiserTweak to configure all the settings for battery performance, your battery life should almost double.
also, does the battery drain fast if you put it in airplane mode?
I know this is not exactly what you are looking for but the program that I have found to be the best is PocketAlarm, it has TONS of settings but I dont think any of them are "sound alarm when device is off"
Check Out
PocketAlarm HomePage