You have to
By the way you don't have to have a thousand saves but I would start saving at least before and after a dungeon. Glitches, bugs and simple errors can mess up your game and cause issues. You need back up saves to insure you don't have to replay hours of content in order to get around them.
I save often as most long term players do.
Edit: BTW welcome to the forums and just in case you haven't recieved one already here is your http://images.uesp.net/c/c4/Fishystick.jpg.
that is incorrect. Typically you would shoot the spinny thingy's paddle to make it spin up and lock. There is no "charging the mechanism with lightning" if anything you just happen to hit the paddles with the lightning bolt which counted as hitting it.
If you are on PC you could open the command console, type "TCL" then press enter. You can then walk through walls and floors. Walk through the gate, open the console and do the TCL thing again, then hit the paddles on the spinners.
If you are on console I guess you gotta fight Karstagg again!
Edit: If you are on console I just had a thought, but I'll need some input from other members on this one. We may be able to trigger the mechanism through the door if there is any spell or shout that can pass through the door and trigger the paddles. I'm not sure what shouts or spells might do that. Maybe try Fus-Ro-Dah or a ice storm spell (I think ice storm passes through things)