[3] Pálinkás competed internationally for Hungary at the age of twenty-five, and simultaneously pocketed his first medal with a bronze in rapid fire shooting at the 1989 European Championships in Zagreb, Yugoslavia.

[5] In 1999, Pálinkás reached the peak of his career on the international stage, as he claimed his first individual gold medal at the ISSF World Cup meet in Seoul, South Korea with 692.7 points.

In his first event, the 10 m air pistol, held on the first day of the Games, Pálinkás fired a score of 570 points to finish in a distant twenty-ninth place from a field of forty-three shooters.

[1][10][11] Pálinkás got off to a bristling start with a perfect 100 on his initial try, until he aimed a rapid, four-second shot poorly at the very end of the first stage that saw him stumble down the leaderboard with a relatively low mark.

He followed his miserable first day score of 287 with a much improved 290 on the remaining half of the competition, but his tally of 577 points was not enough to put him through to the final, forcing him in a two-way tie with Switzerland's Niki Marty for the twelfth position.