basically, the autopilot works under any condition (except certain non-normals of course),.. also, did you ever try to engage AP2 if it fails to engage AP1 ? oh and by the way. If you cant read things on your overhead, you maybe have the wrong resolution or cockpit-tooltips turned off (if you really need them).

As te 737 NG is still an airplane, it can fly also without electrical power, and without engines and apu can still land.In this condition the FMC doesn't work like 99% of the other systems.