There is always hope if the plant is still alive!

Plants like the euonymus growing in containers will need attention a little more frequently than every 5 years :-) While this is not exactly an ideal time to do so, you definitely need to repot. And I'd do some root pruning as well - shave about 1/2-1 " of the rootball off all around and even bit more from the base. Need a good sharp knife or saw for this. Then repot with fresh potting soil (a good quality mix - not Miracle Gro). Add some controlled release fertilizer like Osmocote and water well. You don't really need a larger container necessarily, but it will extend the period slightly before you need to do this again. Plan on doing this about every three years, maybe every second year if staying with same size container.

Thank you - after I do this, how long until I can tell it was a success? i.e. how/when should the plant respond?

Right away :-) You should see it start to push new growth very soon after repotting.

You should see growth unless there was dieback from the winter cold. But you can just cut away what is not leafing out. In a few weeks you should know. And green stems indicate 'live stems'.

before you invest heavily in media.. pots.. and your time...

you might want to price out replacements ... and figure out if rescue might end up costing more than simple replacement ....

the bottom line.. is what your time is worth to you ...

ken