Start by hiring an attorney, and figure out who you want to sue. There is no "election office" of the US. Elections are handled by the Registrars of the various states. As far as whether you have grounds to sue- that is another matter.
5
Washington
There was no US presidential election in 1801. The election was in 1800 and Jefferson was elected and took office in 1801.
The President officially leaves office on January 20th at 12:00 noon after an election year.
generally, the third Monday in January following the election
Ulysses S. Grant
Canidate -US Gov NovaNet
jan 20
Chester Arthur
There was not an election in 2013, it was in 2012. Barack Obama retained the presidential office with Vice president Joe Biden
January 20th following the election. Prior to the election of 1936, presidents took office on March 4 following the election. The 20th amendment changed this.
Inauguration is at noon on January 20 in the year following the election.