I'm developing an application that needs to execute until a count down. When the handled turns off the screen, the countdown halts. How can I continue the execution when this situation happens?
I assume you mean that you want your code to continue executing after the device suspends? First off, you can't. When the device suspends, the processor stops running. You have a couple options though. You can periodically call SystemIdleTimerReset to prevent the device from suspending, run it in "unattended mode" so the backlight shuts off but the device does not suspend, or use an API like CeRunAppAtTime to preiodically wake the processor to run your code.
Note that there's an article on CodeProject.com that contains examples of managed (C#) code for using the Windows Mobile powermanagement features.
http://www.codeproject.com/KB/mobile/WiMoPower1.aspx
Additionally information on starting an application due to various conditions from managed code can be found in a CodeProject.com article too.
There is another way - some "cheating method": Disable sleep mode in Windows Mobile 6. It uses SystemIdleTimerReset and additionally simulates a key touch.