Babchenko qualified as a lone shooter for the Kyrgyz squad in rifle shooting at the 2004 Summer Olympics in Athens. He had been granted an Olympic invitation for his country in the 10 m air rifle by ISSF and IOC, having registered a minimum qualifying score of 593 from his outside-final finish at the Worlds two years earlier. Babchenko started off with his signature event, the 10 m air rifle, where he shot an ill-fated 588 out of a possible 600 to finish in a two-way tie with Sweden's Marcus Åkerholm for thirty-third position. Four days later, Babchenko came up with a much substantial aim to get 591 in the qualifying round of the 50 m rifle prone, vaulting him up to twenty-fourth from his dismal air rifle feat. In his third and last event, the 50 m rifle 3 positions, Babchenko rounded out the 40-shooter field to last place with a qualifying score of 1130 points (393 in prone, 364 in standing, and 373 in the kneeling).