Hi Charles,
First thing I'd do is to clean up the circuit board with some acetone or high concentration isopropyl alcohol so we can see the traces clearly. The physical mount points should be fine for securing a replacement connector to the board, but yeah, you'll definitely need some jumper wires to reconnect the signals.
Hopefully someone will have or know where to get schematics and/or board files for this circuit board; by tracing the signal back we can figure out where to place jumper wires to restore the original signal paths. Alternatively, it is frequently possible to scrape away the conformal coating over the original traces and solder a wire onto the exposed copper to restore the connection, but that assumes the trace is on the top or bottom of the board; if it's on an inside layer then that's not an option.
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