Hi James,
I have some questions about your description.
1.Did you not find the "Install" button?
In this case, you won't see an option to install it until you have an assigned license for Project Plan 3
When you are a user in an organization or school, you may contact the Microsoft 365 admin to assign a correct account to you. Then sign into www.office.com with this account to download and install Project.
More detailed information, please check out the reference: Install Project
2.Or did you find the option to install, but it didn’t respond?
If yes, was there any error message? Please change your browser for a test. Please also check your network and antivirus software.
If I have any misunderstandings, please let me know.