A LL is obligated to provide a clean apartment, compliant with the local codes. In many states, this is the International Existing Structures Building Code (the "IEBC"). When a LL does not provide a safe environment, or a habitable environment, it is said that the tenant is being constructively evicted. In other words, the eviction is by inaction (or failure to repair) as opposed to going to court.
If the condition in your apartment can be recorded in a photo, take ten. Show the photos to someone who has never been to your apartment and ask them to tell you what they see before you clue them in on what is going on. If they cannot see something, a judge will not either.
Step one, where your LL does not repair or provide essential appliances, is to go to the local government to see if they will enforce the code for you. This is a two edged sword. Many a tenant has gone onto this path, only to find the building condemned and their thing on the sidewalk.
Step two, or sometime one, is to write to the LL and provide a written list of deficiencies and a reasonable time to cure the defects. The letter needs to be reasonable since it will be Defendants Exhibit 1 when the LL sues you. The more of these letters you write, the more likely you will be successful if you move out and the LL sues you.
If the LL does not “substantially’ complete the list on time, feel free to move, but tell the LL you are doing so. When looking for a new place, keep detailed records of what you look at. If you are forced to pay more rent, you will be able to file a counterclaim against the LL if you are sued. Your claim will be for the extra rent you must pay for the remainder of the term of your old lease.
Most states will not let you escrow rent until the LL does the work. Philadelphia, but not the rest of PA, is an exception. Seek guidance from a local real estate lawyer if you are confused.