Grand Meridia Apartments in Rahway, NJ, 07065 Landlord won't give money paid in rent back for the rest of the period even after apartment is re-rented RAHWAY New Jersey

http://www.state.nj.us/dca/divisions/codes/publications/pdf_lti/t_i_r.pdf

Page 5 of the above document clearly states that a tenant is not responsible for rental payments for any time that the unit is re-rented at a rent equal to or higher than the current rent.
I moved out on the Nov 22nd. I gave 2 months notice and paid in full till the end of my lease period which was Dec 31st, 2013.

My landlord re-rented as of Mid Dec and yet kept my rent for the rest of the lease term.
I asked several times and initially the leasing agent tried to twist my words saying paying till the end of lease is not "buying out the lease" etc etc.
When I showed him NJ tenant rights, he said that they rented out as of Mid Dec but the tenants did not move in until Jan 1st which is absolutely a cover up because:

1) I called Mid Dec and another leasing agent said that the new tenants were in fact moving in that day (It was a Saturday)
2) My friends in that building confirmed the same
3) They wont show me any official documents to show new tenants have not moved in till Jan 1st.

They never gave me a move in checklist but at move in they slapped me a move out checklist and deducted some money.
What am I comparing move out check list with?

What should I do in this case since they are too greedy to give my money back even though their new tenants were paying them at the same time and they were collecting rent from 2 parties for the same period?

The rent was over $1400. So it's a big deal.