There are multiple numbers answers on this question because of how vauge it is worded: "
How many prisoners died at Fort Delaware during the Civil War?"
The
Fort Delaware Heritage Society cites a higher number of
3074 total prisoner deaths (including 39 civilian prisoner and 109 Union military prisoner deaths):
"
More than 40,000 Confederate POWs, plus hundreds of civilian detainees, and hundreds of Union army prisoners under sentence of military courts-martial were held prisoner at Fort Delaware during the American Civil War. The Fort Delaware Society maintains the most complete index of these men available. Our data base includes information gleaned from microfilmed records pertaining to Fort Delaware purchased from the National Archives, plus information gathered from correspondents and other published sources.
Our Society publication entitled "They Died at Fort Delaware: Union, Confederate, and Civilian" (Fort Delaware Society, June 1997) contains the names of 2,926 Confederate prisoners of war, 39 civilian detainees, and 109 names of Union soldiers who died at Fort Delaware during the war. This represents some 500 more Confederate dead than are named on the Confederate monument at Finns Point National Cemetery, and identifies 4 of the 30 unknown Union dead. It should be noted that these 500 additional Confederate names have yet to be confirmed by obtaining Compiled Military Services Records."
http://www.fortdelaware.org/Prisoner & Garrison Queries.htm
According to the National Park Service website the number is
2,436 who died at the Fort. But that number is incomplete for the Confederates, the Union prisoners, and because there were also civilian political prisoners who were held, and died at the fort during the war. They are not listed on the NPS site, or on the Finns Point Confederate Monument.
"The Federal Government erected the Confederate Monument in 1910 to memorialize
the 2,436 Confederate prisoners who died at Fort Delaware. The 85-foot-tall granite obelisk sits on a low mound and features a bronze dedication plaque and panels listing the names of the prisoners. More bronze panels are set into the earthen mound on all four sides. The Confederate Monument is similar to ones erected at North Alton, Illinois, and Point Lookout, Maryland, sites of other prisoner of war camps."
http://www.nps.gov/nr/travel/national_cemeteries/New_Jersey/Finns_Point_National_Cemetery.html
Edit - Even though you included an answer that is outside the range of 2,400 to 3,000, you cited an authoritative source, so I will count your answer correct.
Hoosier