Because the script runs in the background and invisible to the user, I also suggest testing your script as a background job.
I also encourage you to test your scripts interactively first to verify it works. startup or shutdown, needs to access network resources. One area you might need to test is if your computer script, e.g. Computer scripts should run under the system context which should give you more leeway. Remember that logon scripts run under the credential of the current user and it only makes sense that your logon script perform tasks specific to the user. And while not a requirement, I’m going to encourage you to be running at least PowerShell 3.0. Now before you get to excited realize that your clients must be running at least Windows 7 or Windows Server 2008 R2.