Unless the company has a handbook that sets out that unused vacation pay will be paid upon departure (or you are represented by a collective bargaining agreement), there is no obligation on the part of the employer to pay unused vacation time. You can take them to small claims court, and they are more likely than not to offer a settlement, than continue the process.
The below answer is taken directly from the New York State Department of Labor's website:
Q: When employees resign -- or are discharged -- from a job, must the employer pay them for any accrued, unused vacation time?
A: Whether an employer must pay for unused time depends upon the terms of the vacation and/or resignation policy. New York courts have held that an agreement to give benefits or wage supplements, like vacation, can specify that employees lose accrued benefits under certain conditions. [See Glenville Gage Company, Inc. v. Industrial Board of Appeals of the State of New York, Department of Labor, 70 AD2d 283 (3d Dept 1979) affd, 52 NY2d 777 (1980).] To be valid, the employer must have told employees, in writing, of the conditions that nullify the benefit. .
IF... An employee has earned vacation time...
AND... There is no written forfeit policy...
THEN... The employer must pay the employee for the accrued vacation.
This answer is for general purposes only and does not establish an attorney-client relationship.
Both posters are actually right, although the answers appear different. No law requires you to be paid for not working, i.e. vacation, unless you have some contract that says otherwise. The contract can be established by anything, including testimony. Therefore get as much proof you can of vacation pay, including your own prior pay stubs, and try to make the case.