Here is information from the Illinois State Archives site.
David Bartlett m. Nancy Stinson 9 Jan 1851 in Madison Co. IL.
From the Civil Ward Descriptive list is a man that I think is probably your David Bartlett, even though the age is slightly younger than your 1830 birth date.
David Bartlett, Pvt., Co. G, 83rd Regt., Illinois Infantry Mustered in 31 Dec 1861, for a period of 3 years Age 28; height 5 ft. 10 in; hair brown; eyes blue; complexion fair; Married; occupation farmer, Nativity Madison Co. IL Discharged 19 Mar 1863.
David Bartlett, Co. G, 83rd Regt, Illinois Infantry filed and was approved for an Invalids Pension on 15 May 1882.There were no other filings from his records, no widows pension or pension for minors.Unfortunately, the information about the date and location of his death is not filled in, which is true of many of the Pensions Index cards.Since he was discharged early this information would seem to indicate that he was either wounded or suffered a chronic illness as the result of his service.
IF this is your David M. Bartlett, he was still living at the time of the 1880 census.I have not located him in 1880 but I like a challenge so I am not giving up.