Can you tell me what is going on with this plant and, perhaps, how to save it?
This appears to be a scale insect, probably white prunicola scale. All scale insects suck plant juices and heavy infestations can cause dieback, which is usually preceded by leaf yellowing and premature leaf drop.
Your best bet is to prune out all dry, dead wood. Scrape the bark with your fingernail if you are uncertain. Live tissue would show green beneath it. You can use a soft brush and soapy water to remove as much of the scale covers as you can, and then follow that with a 2% rate of horticultural oil spray.
Plant stems and branches were completely covered so I elected to just get rid of the plant. Now when I replace this plant should I treat the soil to keep the scale from attacking the new plant? If so, how should I go about it?
If possible you should consider planting another species of plant not suscepitlbe to this scale such as inkberry or a holly. There is no treatment for the soil.
If you decide to replant with another cherry laurel all you can do is provide the proper growing conditions and monitor for this scale insect. You may have to provide additional moisture during dry periods. In general, cherry laurels grow best in a well drained soil in morning sun and afternoon shade. Make sure the shrub is not planted too deeply as they can be susceptible to boring insects. These insects are also attracted to thick mulch. Keep mulch no thicker than two inches and away from the base of the stems. Cherry laurels are also prone to the above scale insect. All you can do is provide the proper growing conditions and monitor for this scale insect.