Born in Osaka, Japan, Hideki started racing in karts. In 1982 he competed in the Kansai Kart Land J-class category, winning the championship. He moved up to the Japanese National A-1 class championship in 1983 and won the Japanese National A-1 West Division in 1985. Graduating to the A-2 class in 1986, he once again won a championship.
In 1987 he switched to racing single seaters driving in Japanese Formula Junior 1600, winning 4 times.
Then in 1988 he went into Japanese F3. Driving a JAX Racing Team Reynard 873 Toyota, he came 5th in his very first race at Suzuka, and took another win in round four. He drove in the prestigious Macau F3 event at the end of 1988, and in 1989 Hideki moved to Europe to contest the Vauxhall and GM Lotus series.
He did well enough to get a drive in British F3 for 1990 with Alan Docking Racing in a Ralt RT34 Mugen. He stayed on in F3 for 1991 with the high point of his season coming with a win at Silverstone, the first F3 win by a Japanese driver outside of Japan.
There followed three years in F3000 during which time he made steady but unspectacular progress, though he took a third at Enna in 1994. 'People think I'm useless,' said the ever-smiling Noda as eyebrows were raised when he found a seat at Larrousse at the end of 1994.
He did a neat and tidy job in the Larrousse LH94 Ford, indeed he did a lot better than most people expected. Plans to join Simtek for a series of races in 1995 came to nought when the team folded and to add insult to injury it appears they had taken his deposit.
Hideki then switched to the Indy Lights series, where he was quick but erratic. The highlight of his two years in the States came at Portland in 1997 when he became the first Japanese driver to win a CART-sanctioned event.
In 1998 Noda returned to Japan to race successfully in both Formula Nippon and the All-Japan GT championship, driving the Hoshino team's Ralt in the former and a Toyota Supra with Hironori Takeuchi in the latter.
He joined the Esso Tiger Team Le Mans under Koichiro Mori in 1999 driving another Toyota Supra with ex-Australian V8 Supercar driver Wayne Gardner. The highlight of their season was a win at Fuji.
He continued in Formula Nippon and the All-Japan GT championship though in 2002 he made another attempt in the IRL where he made six starts with Convergent Racing and Kelley Racing. It was back to Japan in 2003 where he continued to race in the National series.
In 2005 he was part of the Japanese A1 GP team for one round at Lausitz, scoring 3 points. He has also drove the Zytek sports prototype in 2006.