I believe that Illinois met its quota of troops in 1861 so Illinois men wanting to serve had to go elsewhere. This URL is the roster of the 3d Battery; you will notice a number of other Illinois men were in the unit.

http://skyways.lib.ks.us/genweb/archives/statewide/military/civilwar/adjutant/3bat/3bat.html

These URLs will take you to histories of the 3d battery:

http://skyways.lib.ks.us/museums/kng/3ksbat.html

http://www.kancoll.org/books/cutler/sthist/milrec-p15.html