Hmm the idea of services is that they run when no user is logged on as well.. but to map the network drive you'd need a user to log on and give credentials, you can set the service to have its own set of credentials..
1. Open the services MMC (a quick shortcut is to click start >> run >> type 'services.msc' )
2. Open the properties for your service
3. Click the 'log on' tab
4. Change from 'Local System Account' to 'This Account'
5. Give it the account you want it to log on as
Now it should work even if no user is logged in locally. It will use the credentials of the account you setup. However I dont think you'll be able to use the mapped drives, you'll have to provide the path \\server\sharename or whatever.