Is the system locked when the task kicks off? If so, this might be the source of your problem. You need to have a logged in, unlocked desktop in order to run most tests that TestComplete executes. If the tests do not interact with the UI at all (such as tests against an API, windows service, web service, etc), then having a locked machine is not a problem. But I believe the workstation does need to at least be logged in.
Could you give us more information to be able to help you better? What does your windows task look like? What command line parameters are you using? How is the task configured regarding what user to run under, etc?