Without any contract that would require a promotion, the employee is not going to get anywhere trying to force a promotion. Even if he was promised a promotion during the hiring process, the employer has broad discretion to change its mind about promotion. In an at-will employment context, where the employer can fire you without cause, the employer effectively has the ongoing ability to change the terms of employment going forward.
If the employee has asked the employer about promotions and is not getting satisfactory answers, or is being told that he is no longer being considered for promotion, his best bet is to start looking for jobs elsewhere. If he finds another position, perhaps his present employer will counter-offer with the promotion and raise he is hoping to obtain.

