Welcome to the forum.
Can you give us a bit more info on how the computers are configured, and I am interested most in where the Project (the New Project, that you created) is located? There are many (too many in my estimation) limitations with regards to networked environments, and that is what one often encounters in an academic situation. The more detail on things like mapped, networked drives, the better. It might be very simple, or maybe not.
In the meantime, take a look at this ARTICLE. It starts with some things that really help PrE run, and then works up through troubleshooting. I hope that we will only need to tweak a few things from the first part.
Good luck, and please let us know a bit more,
One additional thought, that might, or might not play into this scenario, but when one starts PrE the first time, there are two things that happen "behind the scenes." First, there are components of PrE, that get "activated," and this takes some time, plus an Internet connection for the machine. Second, the Organizer, a sub-application that interfaces with PrE (the main program), goes onto the system and catalogs potential media. This can take some time. Some users, with plenty of Assets, think that the program has hung, but it's actually processing potential Assets, and cataloging those. I'd fire it up, and then take a nice long lunch, just to see if that is what is happening.
Are your computers stand-alone computers or are they on a network? If you're on a network or are using school computers, there's a good chance your IT department has your system rights bottled up so that you can't change certain things.
If you are on an individual computer, what operating system are you using? How fast is your processor and how much free, clean, defragmented space is on your C drive?
Also, are you trying to save your newly created project to your C drive or to your network?