Hello jeffburns,
On a regular installation if I set up a new subscriber-role user then upon logging in I cannot see the Events menu (if that’s what you mean) within the admin/dashboard environment – so, if that’s the problem, then it sounds like something peculiar to your installation and the way you have configured things.
I’m not at all familiar with Adminimize so I can’t provide much help here, I’m afraid, but certainly you need to be careful if you edit the capabilities of various user roles.