Barbara,
As Marion mentioned, familysearch.org has excellent records for free, you just need to register with them.
I found these records very quickly at familysearch, which includes a death record for your grandfather that lists his parents' names. (You mentioned on your profile you were unable to locate information about his parents.)
"Illinois Deaths and Stillbirths, 1916-1947," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:N3H8-6NB : 10 March 2018), Alexander Gladkowski, 08 Jun 1943; Public Board of Health, Archives, Springfield; FHL microfilm 1,983,456.
"United States Census, 1940," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:KWT7-DRG : 4 February 2020), Alex Gladkowski, Rockdale, Joliet Township, Will, Illinois, United States; citing enumeration district (ED) 99-59, sheet 15B, line 79, family 272, Sixteenth Census of the United States, 1940, NARA digital publication T627. Records of the Bureau of the Census, 1790 - 2007, RG 29. Washington, D.C.: National Archives and Records Administration, 2012, roll 908.
Find a Grave, database and images,{{FindAGrave|34076856}} memorial page for Alexander Gladkowski (22 Aug 1881–8 Jun 1943), Find a Grave Memorial no. 34076856, citing Holy Cross Cemetery, Crest Hill, Will County, Illinois, USA ; Maintained by Jody Gladkowski (contributor 47255817) .
Enjoy the hunt!