I tried to change my AVG Antivirus service like OP and I received the same error message. At first, I thought of changing registry values in
[HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\*]. As expected, I didn't have the necessary privileges to change the "Start" dword value which corresponds to the "Startup type" options.
I couldn't assign necessary permissions (Full Control) to my user, so I tried a tool called SetACL, which has helped me a lot of times in situations like this. This time however, I wasn't able to do anything. Instead, SetACL reported back to me:
Operating system error message: Access is denied.
It's the first time I encountered something like this. I was hoping to be of more help, but I decided to write down what I tried in case it ever helps anyone.