Electrical – Breaker trips after attempting to install a new outlet

The comments pretty much answer it, but the important take away here is that the wire should possibly be replaced. I was a little thrown by the "speaker wire" comment but I presume you are referring to the light.

Get an electrician in there with a MEGGER to test the wiring. They will determine if it is compromised in areas unseen, and recommend replacing the run if needed.

Be safe! Get the megger. Chances are it melted where you found it, but it could be bad elsewhere, that you haven't found it.

Case 1

If you had a short circuit that popped the circuit breaker and then when reset there is no power I would begin to suspect that a wire connection has become unreliable due to the current surge of the short circuit.

The most likely thing that could be a problem here is if one or more of the wire connections in the circuit consists of the the poke in style terminations. This type of connection is notoriously unreliable. When the wire is inserted a spring tension of a bent piece of metal is all the holds the wire in place.

Over time the string can get weak due to temperature cycling that happens when the contact is asked to deliver relatively high current alternately with relatively low or no current. It is possible that the very high current surge of the short circuit has led to a failure of an already marginal contact.

So I suggest that you check all the outlets on that circuit and see if they are using the poke in style terminations. If so replace all of those with the better quality outlets that have screw terminal terminations for the wires. Some of these will use a wire bent in a loop under the screw head and others may have a clamp device that you insert a straight wire into and then tighten with the screw.

Case 2

Another possibility is that the outlet in question is wired down wind of a GFCI unit that has tripped due to the circuit imbalance in the HOT and NEUTRAL wires when the short of the HOT to the electrical box occurred.

In this case you will have to study the circuit layout to see if there is a GFCI in the circuit someplace.