Here's my theory of the PS2 storyline,
Player wins the race in Palmont City (Carbon Prologue) with a silver Toyota Supra and escapes to Olympic City, events of Underground unfold, player buys a blue GT-R. The events of Underground 2 unfold. Then player buys the BMW M3 GTR, and arrives in Rockport. Events of Most Wanted unfold. Then the events of Most Wanted unfold and after being chased out of Rockport by Cross, he escapes to Palmont City. The events of Carbon unfold. That is where the storyline ends.
The only major plot hole in all this is what happened to the silver Supra?