Well, first off, you say we have it, then you say it can be shut off and turned on it, then ask if we had it at all to begin with. But besides that, and the general oddness of all thought experiments, under those strange conditions: a) You have it because it is something that can be turned off. b) Those moments the computer is on, you have it. c) Those moments the computer is off, you don't have have it. To me, it's equivalent to having a fast-switching narcolepsy, or a very nasty type of epilepsy. Do you have free will when the neurons are firing wrong? Only as much as constraints allow. With overwhelming external influence, free will and brain function itself can be eliminated. I'd consider it a type of sleep or death in that case.