At least you don't have high voltages as a hazard, but replaceing the cable is both the obvious way and a potentially difficult thing to do.
As long as you are sure that damage is confined to the cable and doesn't involve the computer's own socket, then sooner or later you are going to have to open the monitor and see what you can see.
Before that, do make sure that all the pins are there and none is bent or missing.
If you can get at the (monitor end) connections and are able to unsolder or disconnect, then you will need a continuity meter to make sure which pin corresponds to which connection. Make careful notes of which is which. If a conductor inside the cable has broken you must find which one it is and note that too.
All this supposes that you can buy a replacement cable, which should be standard for that sort of connection. It makes me wonder if you would do better to let a legit. repair outfit do it for you, but get a quote first.