All is not lost if you use some patience to work through it.
First question is why was there a short?? That could mean 120 volts got transferred on to the coax. There are lots of screws the the ceiling luan plywood that have sharp points. The factories just run wiring around loose by running it over trusses and letting it lay on the luan. They don't staple it down. Perhaps a screw penetrated romex somewhere and also into the coax? Or maybe romex and coax got pinched together somewhere? Does the coax run directly to a faceplate on the wall or ceiling (the one with the amplifier power button on it)?
New wiring can be run through ceilings, interior walls and inside cabinetry. I've done lots of it - coax, HDMI, romex and low voltage cable. Wire can be fished from opening to opening in a ceiling such as speakers, lights, AC outlets, skylight trim, etc. Luan paneling can be peeled away from the interior wall of a cabinet and wire run in a wall cavity. Look inside a cabinet for where the existing exterior wall jack is and scope out a route to the coax faceplate (or satellite box). It takes plenty of patience to run wiring in a ceiling and walls. Use a fish tape or bent coat hanger wire to pull sections of wire at a time.
You can just abandon the old coax in place. I would really figure out what happened so it won't happen again or do even more damage. Is there an exposed part or damaged romex? Hard to guess at causes without seeing it in person. You *could* possibly trace the existing coax routing through the ceiling by reaching up through some openings in the ceiling and seeing if the entire length of coax was damaged or if you can find the point where the damage happened.
Good luck and don't give up. Maybe some pics would help?