OK first in Design Rules - Routing do you have those layers set in "Selected Layers" to be active for route?
You probably already checked this.
On a related issue I find it rough some times to to route from the top vs bottom also where I have bottom active and
it keeps goign to top to route from when pads are over pads. I sometime have to select the pad hit tab then hit route
to actually route on bottom pad this can be a pain sometimes.
Oh OK I see you can actually get it to start routing on wnated inner layer just can't stop.
I tried same senario here and works fine. I can double click some end point whether trace or pad and it completes.
Sorry I have no other thoughts yet. Has to be a setting somewhere or maybe something in ini file got messed up?