Hello I am a licensed attorney here to help you with your question, please review my response and do not hesitate to ask for clarification
This is an unfortunate situation,
Since you resigned your legal rights would be limited,
however, if you had a contract,
you may be able to claim that they intentionally lied to you to force you to quit your position,
You would have to claim a constructive discharge lawsuit, where you claim that the new employer created such a toxic workplace,
that you had no other option but to quit.
I would retain a local attorney to send them a letter threatening legal action, due to their actions,
the employer may try to settle with you, or come to some accommodation, where you can have the new position.
Without a contract it is harder,
however, if you want to threaten them to see if they will try to settle with you,
consider sending the letter threatening legal action, and that may force them to settle
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