Given the off/on power difference in the vibration, I would think along the line of other's here - that it probably is an imbalance in the powertrain.
But, one of the most common culprits for vibrations at speed is - tire imbalance. So if I were you, I'd start there. Take it down to the local tire discounter (discount tire by me), and have them balance all 4 tires. It will cost you like $15, and take about 20 minutes.
I had an Exploder that had vibration issues on brake from highway speed. I thought for sure it was the rotors warping. Right around that time, I had to get some new tires. And when they went on, the vibration miraculously went away.