If the roots had rotted from over-watering, the stems just above the roots would be mush. They appear to be solid.
Jades fall apart when they get too dry. I suspect that when you re-potted without disturbing the old rootball, you caused a 'shelfing' problem. Shelfing occurs when two different potting mediums are used next to eachother (it usually happens when gravel is put under potting soil in pots). The water runs right by one of the soils (in this case, the old rootball) while soaking the other soil (your new potting mix).
I would cut one of the remaining stems just above the root ball and see how healthy the inside of the branch is. It should be solid and green, no mush, no brown. If the branches are healthy, chances are you can re-root the plant. You can root the pieces that have fallen off and also, I can see little roots on some of the smaller branches. Jades root easily from leaves on up to any size branch.
Put it back into the original pot (or one of similar size with good drainage). Use soil especially formulated for cactus and succulents. The root systems are small - the pot only needs to be big and heavy enough to keep the plant from falling over.
When the leaves are rigid and hard, the plant is happy. If the leaves feel soft, it needs water. Slowly increase the amount of light - if Jades have enough light, the leaves will turn red on the edges.