Do I Have Any Recourse?

You *may* have recourse, but be warned in advance that it is an uphill battle--i.e. winning is not guaranteed, and your odds are likely significantly worse than 50-50.
First, this answer assumes that while you had a written offer, you did not have an actual written employment contract which guaranteed you the job for a defined or set period of time (e.g. a one-year contract). If you did have such a contract, you could sue for what you would have gotten under it based on "breach of contract." But when there is no written contract guarantying you a job for a set or defined period, employment is "employment at will" and you could be terminated at any time--even before the job actually starts.
However, there is a doctrine, called "promissory estoppel," which can sometimes hold non-contractual promises enforceable. To use it requires ALL of the following:
1) You were made a promise (e.g. of a job with certain compensation & benefits) to get you to do something the other side wanted you to do (e.g. take the job and work for them);
2) In order to do what the other side wanted, you had to do something to your detriment (leave a current job);
3) The other side *knew* you'd have to do that detrimental thing (e.g. by telling you to submit your resignation letter, they clearly showed they knew you'd have to leave the existing job);
4) Even though they knew that you'd have to act to your detriment to do what they wanted, they still made you the promise;
5) It was reasonable for you to rely on the promise and act as they wanted (i.e. no caveats, warning signs, they were not hedging or hemming-and-hawing, etc.); and
6) You did in fact act to your detriment.
On paper, you meet the above criteria. But here are the challenges a lawsuit would face:
a) Again, employment is employment at will--the paradigm in this country is that without a contract, no job is guaranteed. Not only are courts often reluctant to overturn that and hold that you had a right to a job when there was no contract, but because employment is employment at will, a court could find that it was simply not reasonable to rely on a promise of employment unless you had an actual contract guarantying it--that is, you could fail item 5), above, because a court could feel that no one should ever rely on a noncontractual employment promise.
b) You got your job back, so your theoretical loss was not getting the previously promised raise. But if you did not have a contract for that raise, it was also not guaranteed--the current employer could have gone back on his word. So it may be very difficult to prove that you actually lost anything, and if you can't prove a loss, you are not entitled to compensation.