To install MIT App Inventor on your PALCS computer, you will either need to find the "Software Catalog" or the "Company Portal" depending on how recently you received your PALCS device.
Company Portal Instructions
Locate the Company portal. (Software Distribution via the Company Portal)
Locate the app listing for "MIT App Inventory." Click on "Install."
It will then install the program to your computer.
After a few minutes a new icon will show up on your start menu.
Clicking on that icon will launch this black window which is exactly what you need.
Software Catalog Instructions
Locate the Software catalog icon. Either on your desktop or start menu. (Software Distribution via The Software Catalog)
Look inside the "PALCS" folder for "App Inventory v 2.3.0" and double click on the icon.
After some time it will add a new icon to your desktop "aiStarter" which means the program has been installed. Clicking on that icon will launch this black window which is exactly what you need.