Not to resurrect a dead thread, but I was having this exact issue yesterday evening and all day today. I put in a ticket last night and never heard back. I destroyed my own ship and spawned at the station and couldnt supercruise away as described.
I did just fix the issue with no help from support. My fix was to turn back around and re-dock at the station, I went into the outfitting on a hunch. My hunch was I would be put in a different "instance" while outfitting. I left the outfitter, and undocked from the station, and targeted a close system hoping the FSD would work. And to my surprise I entered hyperspace. Got to the new system, went to normal speed, was able to then go back into supercruise.
Hope this helps anyone that stumbles upon this thread like I did.
I did just fix the issue with no help from support. My fix was to turn back around and re-dock at the station, I went into the outfitting on a hunch. My hunch was I would be put in a different "instance" while outfitting. I left the outfitter, and undocked from the station, and targeted a close system hoping the FSD would work. And to my surprise I entered hyperspace. Got to the new system, went to normal speed, was able to then go back into supercruise.
Hope this helps anyone that stumbles upon this thread like I did.