Dalbey won two gold medals at the 1988 Summer Olympics in Seoul, South Korea. He won his first gold medal as a member of the winning U.S. team in the men's 4×100 meter freestyle relay, together with teammates Chris Jacobs, Tom Jager and Matt Biondi. He won a second gold medal with fellow Americans Matt Cetlinski, Doug Gjertsen and Matt Biondi in the men's 4×200 meter freestyle relay. Dalbey and his American relay teammates set new world records in the event finals of both the 4×100-meter (3:16.53) and the 4×200-meter (7:12.51) events. While celebrating his victories with Doug Gjertsen in a Korean bar, they removed a marble lion's head wall decoration and were arrested by the Korean police. Dalbey and Gjertsen resigned from the U.S. Olympic team, apologized to their Korean hosts in writing, and no formal charges were filed by the Korean prosecutor; Dalbey subsequently received an 18-month suspension from competitive swimming.
Dalbey transferred to Arizona State University in Tempe, Arizona after the 1988 Olympics, and finished his college swimming career swimming for the Arizona State Sun Devils swimming and diving team. He received four more All-American honors as a Sun Devil swimmer in 1991.
After Dalbey retired from competition swimming, he spent several years as a swimming coach, helping to train other swimmers for the Olympics. He is currently with Main Street Power, a leading solar finance provider based in Boulder, Colorado.