Again, I am sorry to hear about your situation. Failing a valid random drug test could result in a finding of gross misconduct which may then translate to a denial of unemployment benefits. And the fact that it says that there's a no tolerance policy means that they have wide discretion in this regard.
NJ is an at will employment state. At-will employment means that without a contract, you have no contractual or other right to employment with the company. The company is entitled to fire you for any reason: a good reason, a poor reason, or no reason at all--as long as the company does not fire you for an illegal reason (race, gender, age, religion, etc...). But it extends beyond firing, to hiring, promotions, demotions, wage cuts and raises, disciplinary actions, and even scheduling. Unless you can show that this was done in violation of a contract, union agreement, or a clear violation of an unambiguous and binding clause against the employer, or that it was done because of some minority status (age, race, gender, religion, disability) that you have, then they do have this discretion.
So if you can show that they disproportionately targeted you based upon one of these factors, then you might have a case. But in the absence of any proof, I'm sorry to say that you wouldn't have a case against them.
I know this is probably not what you wanted to hear, but it is the law. I hope that clears things up anyway. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable.
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Thank you, ***** ***** luck to you!