Two things to note: 1. 1824 was a 4 man race for the Presidency and nobody had a majority of the Electoral Votes. The House decides the winner from the Top 3 candidates. Clay was in 4th place, but he was also the Speaker of the House. Clay persuaded the House to pick Adams; Adams chooses Clay as Secretary of State. 1828 was just Jackson vs. ADAMS...where Jackson has a clear majority. 2. Nothing was mentioned about his career prior to 1802. He was a diplomat, working as an Envoy (Ambassador) to the Netherlands for George Washington and Envoy to Prussia, under John Adams. He's probably the only person of his era who knew both George Washington and Abraham Lincoln.
Quick correction: there was no tie. What happened is that no individual candidate held an outright majority (more than half) of the electoral votes, so it had to go the House.
4:15 #17. Andrew Johnson served in the Senate after his Presidency and shortly before his death. John Q Adams remains the only President to serve in the House specifically after his Presidency.