Something similar happened to me something like 20 years ago.
Connecting in Dulles (IAD) for San Fran. evening flight. Regular VDB procedure except they said to go to the customer service line to get rebooked, etc. I wasn't experienced at finding the best agent to process the VDB quickly.
Long wait, finally got hotel voucher and meal voucher, but all the airport restaurants were closed. Arrived at hotel ca. 2 AM or something like 4 hours after the plane left.
Happened to get up really early and chose to stand by for early flight that got me into SFO in time for the first meeting of the convention while the booked replacement flight wouldn't arrive until after noon.
Back then the airline (I won't mention the name*) had an advertising slogan, something like "the mark of a great airline is not only how well it moves you in the air, it's how well it moves you on the ground" That night the airline didn't move me on the ground well.
After the fact I wondered, could a GA at a different gate do the rebooking etc.?
Travel tips:
http://members.aol.com/ajaynejr/travel.htm
*If I remember correctly the slogan was done to the tune of Rhapsody in Blue in the background.