What can I do if I resigned from my previous employment, vacated my apartment and relocated to another state to start a new job but have now been terminated?

You may have recourse, but it will be an uphill battle and is far from certain. To begin with, since all employment is employment at will, an employer may terminate employees at any time, for any reason, without having any obligation or liability to them, unless there was a written contract. This applies even if the employee gave up another job or relocated for a job.

Sometimes, even without a written contract, you do have enforceable rights based on the theory of "promissory estoppel." However, for that to be the case, *all* the following must be met:

The other party must have known that you would have to do something to your detriment (give up a job; relocate) to take advantage of a promise they made;

Knowing that, they still made the promise;

It was reasonable for you to rely on the promise (no reason to be suspicious or cautious about it; no warning signs);

You did rely on the promise to your detriment.

Those factors seem to have been met here. But the doctrine of promissory estoppel conflicts with the very strong principal of employment at will. If they had waited longer--a month, two months, or more--and made the decision based on some detriment in your performance, there would be no doubt but that they could freely terminate you: it is accepted that employers may manage their businesses and may terminate underperforming or excess employees.

But what may save you in this case is that the decision was made so quickly, almost immediately, and based on criteria they would have known before offering you the job (i.e. on your experience and their job needs). Therefore, they can't effectively argue that you were not working out. As result, you may in this case be able to enforce some rights on the basis of promissory estoppel, but be aware that:

1) It is not a given you'll win, because of employment at will;

2) Because of employment at will and the fact that they probably feel justified in what they did, it is not likely they will easily or quicly agree to settle, or  pay you something.

Therefore, you are likely going to have to sue (or at least initiate a lawsuit) and you are advised to speak with an employment attorney about the situation--given how much is potentially at stake (relocation costs; possibly several months salary) it is worth while retaining a lawyer to help you. Good luck.