In 1988, Duke actually did run for president as a Democrat, then as a Populist, switching his party affiliation to Republican that December. It was as a Republican that Duke was elected to the Louisiana legislature in a special election in 1989 (my cartoon about that is here). The next year, he ran for Louisiana's seat in the U.S. Senate and polled ahead of Republican Party-endorsed Ben Bagert; to avoid a run-off between Duke and the Democratic incumbent J. Bennett Johnston Jr., the GOP pressured Bagert into withdrawing from the race. Johnston won reelection.
Duke was back again in 1991, running this time for Governor. This time, he beat incumbent Republican Buddy Roemer in the primary, forcing a run-off between Duke and the ethically challenged Democrat, former Governor Edwin Edwards.
Polls predicted an Edwards victory, but Duke countered that his supporters were merely reluctant to be honest to pollsters. In the end, a record 1 million votes were cast for the twice-indicted former Governor, versus only 671,000 for the klansman.
Duke tried running for President in 1992, this time as a Republican; but the GOP fought to keep him off the ballot, and there was already a much more prominent national figure who could appeal to the Duke Voter.
The high point of Duke's career was already behind him. Duke would later join the Reform Party to work on Pat Buchanan's 2000 presidential campaign. (Donald Trump explored running for the Reform Party nomination that year as well, but dropped out to host "The Apprentice" instead.) Since then, he has offered his support to various fascist and anti-Semitic politicians in Europe and the Near East.