1. As for the $1850. deposit, either call your bank or go online and see if the check was deducted (cashed). If it's not deducted yet, put a stop payment on the check. You will pay a fee for this, but the broker is out the money.
2. To contact the landlord directly, does your building have a property management company? Call them and ask for the name or phone number of the owner / landlord. You can also register your complaint with the property management company. You don't need to go thru the broker.
3. New York City is very tenant friendly - the laws favor tenants - not landlords.
4. Tell the broker that you will be happy to write negative reviews all over the internet. If your rental was located outside NYC, the normal method would be to speak with the Office Manager / Broker in Charge and if necessary - contact the local / state Board of Realtors. However, in NYC, this is a waste of time and won't get you points because in NYC, brokers, their managers and REBNY all stick up for each other. The NY State Board of Realtors doesn't do anything for NYC either. Your best bet is to write negative reviews online because that puts agents on notice since future renters read reviews and it forces the agent to change their behavior + you get a solution much faster.
5. You may need to take a day off work but go to the New York City Housing Dept, and fill out a complaint form for the $1,850. deposit. Not sure what the next step will be but the Housing Dept. will act on your behalf.
6. Hope you find a new job soon. If it helps, you should expand your search to ALL of New York City and the nearby suburbs. Look at it this way, in Westchester County search White Plains, Yonkers, New Rochelle, Tarrytown, Eastchester, Scarsdale, etc. - all are places that have jobs and housing is much cheaper than anywhere in New York City. Also try Nassau County (Long Island) - plenty of places / towns with jobs and housing is much cheaper than New York City.
For transportation - the suburbs do have buses that run frequently and they go to New York City too. Also there is the commuter railroads - Long Island Railroad to Penn Station or MetroNorth to Grand Central. From most suburban towns it takes 30 minutes during rush hours (express trains).