You don't sound dim. Don't worry about that.
When you see Spybot-Search & Destroy 2.7, Administrator Privileges at the top, that should be when Spybot is in administrator mode. Some modules(the different parts of Spybot within the start center, like system scan, etc.) will prompt you to run them as administrator if needed, some will not if it's not really necessary. To get all the modules to be run as administrator, just rightclick the Spybot start center and select Run As Administrator, then say yes to the prompt. Actually, could you run Spybot as administrator now, make sure it says Spybot-Search & Destroy 2.7, Administrator Privileges at the top, then click "More Details" on the bottom right. Does it still say Update service stopped?