Hello-

Found the following in the Illinois Death Index:

Name: Andrew Stolberg
Date of Death: 21 December 1935
Place of Death: City of Moline, Rock Island County
Age at Death: 84
Death Certificate # 0048970

Certainly can't say for sure that this is the Andrwew you are seeking as if the age at death listed is correct it would put his year of birth at 1851 not 1861 as your post indicates. My guess would be that there was a transcription error somewhere and this is your Andrew as the name, geographical location, and general time frame are the same as your Andrew. Just too many coincidences here!
Should you see fit to pick up a copy of his death certificate they are available from the Rock Island County seat (City of Rock Island) or the Illinois Dept. of Public Health in Springfield, Illinois (state capital).

Hope this helps. Good Luck in your search.
Paul