Molyneux began his TT career at the 1985 races but did not record a finish until his fifth outing at the 1987 event, where he placed tenth in the first leg before retiring from the second. Progress came steadily, with a sixth-place finish in the first leg of the 1988 Sidecar TT preceding a retirement in the second.
The 1989 meeting proved the turning point. Campaigning a Bregazzi Yamaha and partnered by experienced passenger Colin Hardman, Molyneux claimed his maiden TT victory in the 'A' race and finished third in the 'B' race, earning overall victory in the 1989 Sidecar TT. From that point forward he became a fixture at the top of the sidecar results.
Molyneux's accumulation of victories came across multiple decades and with multiple manufacturers. One of his most celebrated achievements came in 2012, when he became the first competitor ever to win TT races using all four major Japanese manufacturers' engines — Yamaha, Honda, Suzuki, and Kawasaki — across his career. His 14th win had come in 2009 aboard a Suzuki-powered machine, which also made him the first winner of an Isle of Man sidecar TT on a Suzuki. He returned from a 2011 absence to claim a double victory in 2012 on a Kawasaki, bringing his total to 15 at that time, before adding further wins to reach 17 by his 2014 victory in the second sidecar race of that year.
By 2015 he held the absolute sidecar lap record for the Snaefell Mountain Course, set with a time of 19 minutes 23.056 seconds at an average speed of 116.785 mph.
In 2006 Molyneux and his passenger Craig Hallam crashed during Thursday afternoon practice at Rhencullen after their sidecar outfit experienced what was described as a 140 mph "bluebird-style flip." The outfit was destroyed in the resulting fire, and Molyneux was too badly injured to compete in the actual races that year. He made a full comeback in 2007 and took a double victory, adding two more wins to his record.
In 2013 a right-hand bend on the Snaefell Mountain Course at the end of the Cronk-y-Voddy Straight was officially named Molyneux's in recognition of his victories, with the same honor extended to fellow TT great John McGuinness.
Away from racing, Molyneux is also a builder of road-racing sidecars under the marque DMR — Dave Molyneux Racing. He has supplied sidecars to numerous other TT winners, including ten-time winner Rob Fisher, 2006 double winner Nick Crowe, and multiple FIM World Champion Tim Reeves.
In 2016 a documentary film, 3 Wheeling, captured Molyneux over the TT period of that year. The film premiered in May 2017 and received a limited theatrical release in Northern Ireland, Germany, and the Isle of Man. Earlier, in 1994, Molyneux choreographed and performed the motorcycle stuntwork for the art film Cremaster 4 by Matthew Barney, the opening chapter of Barney's acclaimed Cremaster series.
Often known simply as "Moly," Molyneux has embodied sidecar racing at the Isle of Man for over 35 years. His combination of riding skill and mechanical knowledge — reflected in the DMR chassis he designed and built — sets him apart as both competitor and constructor. No sidecar racer has won more TT races, and his name is now permanently inscribed on the course itself.