Fulop was brought to England from MTK Hungaria for a small fee and slipped into the Spurs reserve side.
Radek Cerny was favoured as the back up keeper to Paul Robinson, but Fulop got a place on the bench at the end of season 2004-05, when Robinson got injured.
Spent successful loan spells at Chesterfield and Coventry City, where he spent most of the 2005-06 season, when he expounded his desire to get away from Spurs to play first team football.
He finally got his wish on 2nd January 2007, when he signed a £500,000 permanent deal with Sunderland, where he had been on loan, as Black Cats keeper Ben Alnwick moved in the opposite direction. Had a reasonably successful time there when selected, but fell out of favour when Craig Gordon was signed by Steve Bruce, going out on loan to Leicester City and then a dream loan to Manchester City for the last month of the season, featuring in the penultimate match of the season at home to Tottenham Hotspur in a game that decided who would be playing Champions League football in 2009-10. Spurs won 1-0, with Fulop having a good game, but he was not kept on and returned to the Stadium of Light.
During the close season he was allowed to leave for free to join Ipswich Town and was their first choice keeper for much of the season, but with a change in management, Marton left in the summer of 2011 to join Premier League West Bromwich Albion on a free transfer. His debut was a disaster for Tottenham, coming in the last game of the 2-11-12 season, when he gifted two goals to Arsenal, allowing them a victory that kept them above Spurs in the table.