How do I disable resident protection?

I went into Advanced Mode, Tools and Unchecked "Resident", but it still runs every time I boot my computer.

Which version of Spybot-Search&Destroy are you running?
Have you tried to right click on the icon in the taskbar (lower right hand corner), exit TeaTimer, go to Advanced Mode to make sure the box is unticked and reboot?

Just go into the Windows Services console and set all Spybot services to Manual.

Just thinking out loud.Have you unchecked the right Resident Protection?

In Spybot 1.6.2 and below,there should be two Resident protections listed:
Resident "SDHelper" and Resident "TeaTimer".
Resident "TeaTimer" is the one that runs and shows in the notification area down by the clock on windows startup.You'd want to make sure that one is unchecked.