Benefits are not usual for those that quit.
An employer need not allow a person that has resigned to fulfill two weeks or any period of notice.
As an at-will employee, you can quit at any time for any reason, you can be fired for any reason, a rotten reason, or no reason, except unlawful discrimination. If you do not have an employment contract or union to represent you, your recourse is limited. Discrimination based on age, gender, race, religious beliefs etc.... may give rise to a different answer.
You might find my Legal Guide helpful "Workplace Discrimination: A Basis for Wrongful Termination Claims"
You might find my Legal Guide helpful "How to Choose a Lawyer for you.”
You might find my Legal Guide helpful "What Do I Tell My Lawyer"?
No one can know what the record is in the case because online we cannot find out any details. Check with a lawyer in your locale to discuss more of the details.
If you have a discrimination theory about retaliatory discharge or hostile workplace conditions you'll need a lawyer. Religious belief, age, gender, race etc. all are discriminatory reasons for which you cannot be legally fired and upon which you might base a wrongful termination suit.
Good luck to you.
NOTE: This answer is made available by the out-of-state lawyer for educational purposes only. This observation is not like a communication with a lawyer with whom you have an attorney-client relationship along with all the privileges that relationship provides.
You can file for unemployment and should do so. There are cases where unemployment was awarded under the facts that you state. ( see W. Jordan v. Morrison, 656 P.2d 445, 446-447 ( Utah, 1982) (employee was discharged and did not leave work voluntarily where employee gave resignation letter dated November 26, 1980 stating his last day would be December 10, 1980, but employer immediately accepted the employees resignation, making it effective the day of his letter). It will depend, of course, on the unemployment case law, and statute, in the jurisdiction where you file. You should seek the advice of an attorney in your state to see where to file. Good luck