Normally, unless you had an actual employment contract specifying your start date, your employer could change, delay, defer, etc. that date at will. (If you have an employment contract, it is enforceable, like any other contract, and you could, for example, sue for the compensation you are owed under it.) That is because in the absence of a contract, the law will not generally enforce promises; rather someone, like an employer, may change or dishonor its promises, like a promised start date, whenever it wants.There is exception, however, if you can establish the requirements of "promissory estoppel"--in that event, the promise may be enforceable. To be enforceable, you'd have to show all of the following:1) To take this job, you would have to do something to your detriment--like leaving an existing job.2)  The employer knew, at the time, they made you the offer, that you would have to leave the other job to accept a position with them.3) Knowing that you'd need to leave the other job, they nonetheless made you the job offer, intending that you would take it and give up your other job.4) It was reasonable for you to rely on their offer--that is, no reason to think it wasn't a valid offer.5) You did in fact rely on their offer in leaving your job.If you can establish all these elements, you would have a good chance of holding them to their promise--i.e. of obtaining compensation from the date you were supposed to start. You would have to sue them to do this, however, if they will not voluntarily pay you.