Does the program need any input from you or does it just sit there and send out the magic packets at a certain time?
Does the program close automatically once all of the computers have been turned on or do you manually have to close the program window?
My suggestion if it does not require input but needs access to the network is to run it as a scheduled program like normal using the Network Services account. This will allow it access to network resources. It still will not pop up any window as it sounds like it may be a DOS or command prompt based program only, but as long as it requires no input, this is fine. The only downside is that you will not be able to monitor the normal program window that you would see if you were to run it from within a regular user account.
The other option is to look into a newer version of the program that is compatible with Window 7/Vista/2008 and that has a full GUI or a built in scheduler.
IT Desktop & Network Consultant - MOS Master Certified, MCP, MCSA, MCITP - Windows 7, CCNA Certificate Pending, A+, Network +