Instead of the planned upgrade we were going to perform, we decided to start from scratch and do a full reinstall of our environment. So that entailed registering the Dell EqualLogic HIT Kit to a new VirtualCenter.
Start off by opening up the console on the VM and logging in. (Default Username: root Default Password: eql) Once logged in, select Option 8 to unregister it from the old vCenter.
From there, select Option 4 to configure vCenter. Enter in the credentials for the new vCenter (IP, admin account, password, EQL HIT Kit Appliance IP, and an admin email addres), confirm the credentials and the appliance should connect to vCenter and be successful.
Once back to the main screen, select Option 7 to register the appliance with vCenter and then reboot the appliance
After the appliance is back at the login prompt, check back to the vCenter "Solutions and Applications" section and make sure that the EqualLogic utilities are there. For good measure, login to one of the utilities and ensure the configuration is correct.