Firstly, go to 'Start > Settings > System tab > Backlight'. There, in one or more of the tabs, you will find checkboxes named 'Turn off backlight if device is not used for', next to a dropdown menu representing the timeout value, for operation both under battery and external power sources.
However if you find these settings to be correct, and, yet, your device refuses to follow them, I think something you have installed might have messed them up. Perhaps a hard reset would fix your problems. A hard reset will restore your device to its factory defaults, i.e. all the programs you have installed, as well as your personal data, will be cleared. So, if possible, make a backup, to be restored afterwards.
If your device is operational, you can hard reset it by going to 'Start > Settings > System tab > Clear Storage', type in '1234' and, then, tap 'Yes'
However, if you are e.g. stuck in the splash screen phase, you can still hard reset your device by hardware means: press and hold both softkeys (the ones marked with '-',) and, then, whilst keeping them pressed, briefly press the reset pin with the stylus pen. Release the softkeys only when instructions come up on-screen. Press the green Send/Call button to confirm the procedure.
Hope you are able to sort your problems out.
Cheers! Carlos