I've done a quick search and I "may" have found your ancestor. The only "Isaac Adams" who died during the war and is listed as married, lived in a community just south of Danville.

Name ADAMS, ISAAC N
Rank SGT
Unit 125 IL US INF
Company K
Residence GEORGETOWN, VERMILION CO, IL
Personal Characteristics
Age 27
Height 5' 11
Hair BLACK
Eyes DARK
Complexion DARK
Marital Status MARRIED
Occupation FARMER
Nativity GEORGETOWN, IL

Service Record
Joined When AUG 13, 1862 Joined Where CATLIN, IL
Joined By Whom G W COOK Period 3 YRS
Muster In SEP 3, 1862 Muster In Where DANVILLE, IL
Muster In By Whom N/A Muster Out N/A
Muster Out Where N/A Muster Out By Whom N/A
Remarks DIED NOV 4, 1864 FROM WOUNDS RECD IN ACTION AT CHATTANOOGA TENN

This man's widow and minor child both applied for survivor's pensions. If you'd be interested in obtaining these files, please go to http://history-sites.com/research/index.html , where you can order them online or by mail order or click on the link below.

Jim Martin