Your original question was somewhat overlong and there was quite a bit about how careful you had been. From this distance and not seeing your machine it goes like this.
It should take considerable force to pull the hose from the machine if it was (a) designed properly and (b) fitted correctly. Given that the power failed at the same moment that the hose popped out then it is reasonable to assume that both events may well be connected.
If you tug hard enough on the hose (hard enough to pull it out) you are also tugging with the same force on the power cord IF the power cord is trapped - like under a door for instance.
I am unable to see your machine but if it were mine and if I were trying to repair it I would first suspect the integrity of the cord - particularly the wire attachment at each end. I would also feel the cord itself for any signs of interior damage and snapped conductors inside.
As you say in your hunch..."some reason the current is not getting to, or is not being allowed to get to, the motor."
It's my hunch too - which is why I suggest you check the cord - the most likely failure area even without the gentle tug and hose pop.
Even if you really, really, really did just pull the hose gently I think it's still a good idea to check the cord first - before you dismantle the machine - it's a quick and simple thing to do at zero cost.
Have you actually checked the cord yet?
Peccavi
December 2008