Since it is a permission error, there are two things you can try.
In the start menu search, type in 'UAC', and press enter.
Drag slider to the top.
Now try to start the service. If that fails, try my next method.
In the start menu search, type in 'cmd', and press 'Ctrl' + 'Shift' + 'Enter'.
Click yes if prompted.
Type in the command prompt
net user administrator /active:yes
and press enter.
Close the cmd window.
Log off, and you should now have a new profile. Click on it to log in.
(This account gives you the highest privileges)
Now try to start the Security Center service again.