First, at least IMO you should talk to the IT department at your university or company. It's ridiculous that you can't run downloaded software like Protege. If you are doing computer science research you aren't going to get very far with those kinds of restrictions because there are so many great freeware tools that you also won't be able to download and run in addition to Protege such as the Eclipse IDE. I don't know that much about the admin side of things, someone please correct me if I'm wrong, but I don't think Protege requires any kind of additional authorization beyond what any other downloaded piece of software would.
You might want to double check your own security settings, especially if you are on a Mac. I do most of my technical work on Windows these days but when I was still using my Mac for Protege, I noticed the Apple OS was getting more and more restrictive so if you wanted to download software that didn't come from the Apple App store you had to go into your security settings and change them, the default setting was only applications from the App store could run and at least once I remember the changes I made were over-written when I installed a new version of the OS and I had to redo them.
But in the mean time you can at least use the WebProtege version. That's a completely hosted service at Stanford so it's just like any other web site:
https://webprotege.stanford.edu/ Just create an account. This will significantly limit how much benefit you can get from Protege however. As of this time there are things that only the downloaded desktop version of Protege can do, most importantly the WebProtege version can't currently run any reasoners and reasoners are what makes Protege really powerful as opposed to being just a good modeling environment.
Web Protege is great when you have a team that wants to collaborate on an ontology or when you have an ontology that you want to share with people but to really understand what can be done with OWL, SWRL, etc. you need a reasoner which at this point means you need the desktop version.
Jenny, one other thing that occurred to me: there is a minor bug in Protege where the exe file stops working for some reason. You might try the following: navigate to where the .exe file is on your computer, it should be under a directory called Protege-5.5.0 if you are using the latest version. Try double clicking on the "run.bat" file which should be in the same directory. That might bring up Protege for you. I have that problem myself, when I modified the amount of memory that my version of Protege uses the exe file stopped working but using the run.bat file is an easy work around. I hope that's what it is, much easier than having to argue with your IT people.