Beth -
I am not sure what airline you are flying and if this applies in this situation but there is a Rule 240 that applies to all airlines
If your flight is cancelled or delayed for any reason other than weather, rule 240 says airlines should put you on the next available flight on any airline at no extra charge.
I use this rule a lot - if I am on a flight that is delayed - I always ask what other flight they can get me on (this is how I end up flying non-stop a lot even when I booked with a layover)
It seems to me that if you have a confirmation in hand that says you are on a non-stop flight that they have to keep you on one even if it is not on their airline and regardless of cost - I would call and ask them what happened to your flight and if they say they cancelled it - I would say that you booked a non-stop and you do not want to arrive any later than originally planned and that you either want an earlier non-stop on their airline and if they don't have one then you would like one on another airline
at the very least I would tell them that you paid for a non-stop flight and if they are not able to provide one you would like some sort of compensation
here is a link to rule 240 - you should always carry a copy of it for your airline when you fly
http://www.mytravelrights.com/travellaw.cfm?ai=3