There are a few possibilities but a correct diagnosis will take more than an online forum can manage! Cut off that branch that has the wilted leaves and take it and these photos to your county extension office and ask for their help. They may be able to tell just from examination what's up or they will forward to their plant pathology for diagnosis.

It won't hurt to prune off and obviously dead branches and take them as well, starting as low on the trunk as you can. Be sure to sterilize your pruners between any cuts.

Thank you Gardengal! Let me ask this: the brown area I zoomed in on - where branches connect - is that normal coloring for such an area or would that be an indication of an unhealthy branch? I'm not seeing any obvious dead branches to cut and bring in right now (assuming the dead leaf area isn't a dying branch, since it's green when scratched), that's why I ask.

Green under the bark is not a reliable test of the branch being alive. It takes time for dead issue to lose enough moisture so the wood is dry and brown but the wood will still be dead during that period. What is a better way to judge is a) there are no leaves on the branch or sign of leaves to come; b) no sign of any viable, plump buds on the branch/stem and c) the branch or stem looks dull and gray or off-color rather than the more typical reddish brown.

And yes that discolored patch does not look good, considering the appearance of wood present on the portion exterior to that patch. It looks shriveled and off-color.