I had this problem on a computer I used exclusively to remote into. I never resolved the problem despite trying a few things I read in this thread.
Later, I moved a different computer I had been logging into successfully for quite a while. When I moved it, I didn't plug in the monitors, mouse or keyboard. I figured I wouldn't need it for a while so I didn't plug them in. I tested GoToMyPc and it worked fine.
Later, when accessing from a PC different from the one I tested on I started having display and mouse issues. The display issues were resovled by plugging in the monitors (to the host) with power (though monitor power doesn't need to be on).
My mouse issue was resovled by plugging in a mouse to the host.
It seems as though with certain computer interactions it is best to have all hardware plugged into the host, even if you don't intent to use the host locally.
As it turns out, the first computer I mentioned didn't have a mouse installed either.