What the OP experienced appears to be what Delta refers to as a "Schedule Irregularity." Their contract rules on this state:
C) Schedule Irregularity
When a passenger will be delayed because of a schedule irregularity or a carrier cancels the passenger's reservation pursuant to Rule 135 (cancellation of reservations)
1) Any carrier causing such delay or in the case of a misconnection the original receiving carrier(s) will transport the passenger without stopover on its (their) next flight on which space is available in the same class of service as the passenger's original outbound flight at no additional cost to the passenger; if space is available on a flight(s) of a different class of service, acceptable to the passenger, such flight(s) will be used without stopover at no additional cost to the passenger only if it (they) will provide an earlier arrival at the passenger's destination, next stopover point or transfer point, or
2) If the carrier causing such delay, or in the case of misconnection, the original receiving carrier(s), is unable to provide onward transportation scheduled to arrive at the passenger's final destination within two hours of the passenger's original arrival time, any other carrier or combination of connecting carriers, at the request of the passenger will transport the passenger without stopover on its (their) next flight(s) the same class of service comparable or lower to the fare paid as the passenger's original outbound flight or if space is available on a flight(s) in a lower class of service, acceptable to the passenger, such flight(s) will be used without stopover at no additional cost to the passenger only if it (they) will provide an earlier arrival at the passenger's destination, next stopover point or transfer point, or
EXCEPTION 1: Delta shall have no obligation to accept another carrier's ticket which does not reflect a confirmed reservation on Delta, unless the issuing carrier reissues the ticket for any changes in routing. In the event such carrier is not available to do so, Delta reserves the right to reroute passengers only over its own lines between the points named on the original ticket.
EXCEPTION 2:
I) Passengers holding flight coupons for free transportation will not be transported on Delta flights. This provision is not applicable to tickets issued by a
travel agent on behalf of a defaulting carrier and accepted by Delta pursuant to agreement CAB 270L0 (DEFAULT PROTECTION PLAN) and Rule 240 F).
II) Delta reserves the right to accept tickets under this rule issued at fares other than the full adult one-way first class (F/F06), coach (Y, Y06), fare for transportation on Delta flights only if space is available at the time of departure of such flights.
III) Delta will not accept tickets under this rule issued by another carrier which, as of the time such ticket is offered to Delta for acceptance, no longer has a valid interline agreement with Delta.
EXCEPTION 3: Passengers holding tickets for another carrier will be accepted on Delta first class service upon payment of additional fare to the level of Delta's applicable one-way First Class fare.
EXCEPTION 4: Schedule irregularity does not include force majeure events as defined in paragraph G).
3) The carrier causing the schedule irregularity will refund in accordance with Rule 260 (Involuntary Refunds).
As far as compensation, if you are coach or business class, the only thing Delta's contract offers is one 3-minute station-to-station call within the continental U.S. No meals.