I've seen a great post on this site about using a PowerShell script to use a batch file to unzip a file:
How can you zip or unzip from the script using ONLY Windows' built-in capabilities?
But I cant find anywhere about how to use PowerShell with a password protected zip file using only Windows native zip - no 7-zip or likewise since I can't install stuff on my work machine.
Since I could not find it in Google I'm a little worried it's not possible.
In Windows 7 and later it is not possible; the password capabilities were removed. I have heard (but never confirmed) that this was instigated by the EU anti-Microsoft actions, claiming that it was anticompetitive (against WinZip et alia).