That doesn't sound impossible to repair.... Can you take a macro shot of the damage?
Did the connector came off the circuit board? Do you have the skills and the equipment to deal with the task? I would probably NOT try taping it as it will very likely result in connections unreliable at best. You could often scrape the surface and expose the copper, then use a very small amount of solder to bridge the broken part. But then again, I'm saying all this without knowing extent of the damage.