Sincde you are going to need a certificate duly issued and stamped by auithorities in Argentina you wouod need to know spanish and fillut forms and pay fees so you woulod be better off going to an english speaking agency at www.familias-argentinas.com.ar
It used to be easier to obtain entry records to get thecorrect spelling and year of birth which he used tonter Argentina. I checked with the current Argentina telephone directory at www.telexplorer.com.ar and put in ILIC in the upper left box that said "APELLIDOS"and nothing else and then click "BUSCAR" for all the spellings of the ILIC family names which are ILIC-ILICH-ILICIC-ILICZ (about 20 names in all) just so you know to make sure of thre spelling of your person of interest.
Since you did not give me any information about him (marriage, children where he lived in Argentina etc) or relatives in Argentina this is the best I can do for you. Petertimber