Ms. Lynda, there is no Isaac Dyer listed in Booth's Record of Louisiana Confederate Soldiers, the Louisiana Confederate Pension Database or the National Park Service Civil War Soldiers & Sailors System.
There were 17 men named Issac Dyer who served in the war according to CWS&SS. Most appear in Umion units. This leads me to believe your Isaac Dyer wasn't in the military. He may have held a job or position that would have exempted him from service or his age possibly prevented him from serving. His family may have been Unionist as well.