If you look on the label of the AC adapter it will give you it's input/output numbers. You typically want to find something with the same voltage and same or higher amperage rating.
If you are handy with a meter you can check the one you have to see if it's blown, which (if it were plugged in) probably is due to shorting out.
You should be able to splice the wire back in unless it's some strange shielded cable or similar.
We had out cat and dog chew a lamp cord. IDK what was so attractive about it, but once they both got a good zap (the dog actually threw the breaker) they didn't mess with it any more. The dog wouldn't even walk near that area.