OK, here isthe infoI found about NJ:
Copy-paste parts of this website: http://www.lsnjlaw.org/english/placeilive/rent/tenantsrights.cfm
Moving out because of bad conditions
If your landlord refuses to make needed repairs to your apartment, you can move out before the lease ends and still not be held responsible for rent for the time left on the lease. It is important to have proof of these bad conditions. You can get this proof by having a building inspection done and taking pictures before you move out. In this situation, the law holds the landlord responsible for breaking the lease by failing to fulfill his or her duty to provide you with safe and decent housing. This is called constructive eviction. Please read Chapter 6, Your Right to Safe and Decent Housing, for an explanation of a landlord’s duty to maintain housing in good condition.
There are certain rules that apply for a constructive eviction.
- You can break your lease under this rule if the conditions in your rental unit are so bad that it is very hard to live there. Examples of this are if you have no heat in the winter, or your health and safety are at risk. In addition, your landlord must have failed to correct the problem after receiving notice from you, which should be in writing if at all possible. Cite: Marini v. Ireland, 56 N.J. 130 (1970) C.F. Seabrook v. Beck, 174 N.J. Super. 577 (App. Div. 1980).
- If you move because of bad conditions before your lease ends, your landlord may sue you for rent for the time left on the lease. The landlord will almost certainly refuse to return your security deposit. You may find yourself in court either because the landlord has sued you for back rent or because you are suing the landlord for the return of your security deposit. Whether you win or lose in court will depend on how serious the judge believes the conditions were that you claim forced you to move. Judges usually allow a tenant to break the lease only when very serious conditions exist, such as no heat, no water, a broken toilet, a broken elevator, flooding, or excessive and constant disturbances.
- It is important that you give the landlord notice of the defective conditions and a reasonable amount of time to make repairs before moving out and claiming constructive eviction. Your notice should be in writing, and by certified mail, return receipt requested. Keep a copy of your notice.
- If serious conditions in your apartment force you to move before the end of your lease, you are still entitled to have your security deposit returned to you.
Chapter 6: Your Right to Safe and Decent Housing
Housing must be safe and decent
Tenants frequently complain that their landlord will not repair such things as windows, locks, toilets, faucets, and heating systems when these break from normal wear and tear. Tenants also complain that their landlords do not do routine maintenance, such as pest extermination. You have a right as a tenant to live in housing that is safe, clean, and decent. This chapter explains this right and the laws that place a duty upon your landlord to maintain your rental unit in good condition. This chapter also explains the different steps you can take to have your landlord make needed repairs and do routine maintenance.
There are several different laws that require landlords to maintain tenant-occupied rental property in safe and decent condition.
The warranty of habitability
Landlords have a duty under New Jersey landlord-tenant law to maintain their rental property in a safe and decent condition. This duty applies to all leases, whether written or oral. The duty to keep rental units safe and decent is called the warranty of habitability. The warranty of habitability is based upon common sense: in return for paying rent to the landlord, the landlord must make sure that the housing is fit to be occupied by the tenant.
The warranty of habitability has been held to include keeping the basic elements of your housing unit in good condition. This includes taking care of physical elements, such as the roof, windows, walls, etc. the systems that supply you heat, hot and cold water, and electricity and gas appliances, such as the stove, refrigerator, and dishwasher keeping apartments pest-free and common areas clean and providing security against crime, such as locks on doors and windows to deter break-ins.
There are more info on that web site, but it does look to me like you have rights. But the problem is that you may end up having to sue your landlors in order to get your security deposit back.  Maybe you should contact these people:
New Jersey Tenants Organization
389 Main Street
Hackensack, NJ 07601