Acceptable to fix an open ground like this: ?

Hi I was recently installing a new ceiling fan and discovered that the circuit has an open ground, then discovered that all boxes in the circuit are open as well. I found two places in the attic where the ground wires were left un-spliced (looked like on purpose), thought that was it for sure but negative. So I assume that the ground is not connected where it originates, at the panel. Do I need to trace this cable (not very accessible) back to the panel to fix OR can I cut another run of cable (different circuit) in the attic with a known good ground, put in a junction box and tap into the ground, then run a single ground wire from that junction box to the three boxes with the open ground that are all fairly accessible?