You are apparently a rank amateur at being a landlord and you should sell the place and get out of the landlord business.

Here's why.

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Tenant broke 6 month lease and now does not want to pay me. Tenant has 6 month lease that runs thru February. They just moved out on me. They have not paid the water bill since they have lived there nor 2 month of utilities. Also owe one week of rent. It is all stated in lease that they are to pay this.
Amateur mistake number 1:

You should have served them a pay or quit notice the absolute minute that they failed to pay what they were supposed when they were supposed to pay it and follow up with an eviction in court when the deadline of the pay or quit notice came and went.

Quote Quoting inmom
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Now I am stuck because I kept them in my name and they were to pay me.
Amateur mistake number 2:

NEVER keep the utilities in your own name. Put it in your lease that the tenants get the accounts set up in their own name by the time they take possession and that you are taking the accounts out of your name the day before possession.

Quote Quoting inmom
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Also owe one week of rent.
Amateur mistake number 3:

Always serve your pay or quit notice immediately the day after the day a tenant defaults on rent.

Quote Quoting inmom
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In October they informed me that the heating did not work. I offered to have it looked at
Amateur mistake number 4:

You don't OFFER to have it looked at. You say "I'll have a repairman come over today." Then you call a repairman and just get it done.

Quote Quoting inmom
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they did not want me having someone come in when they were not home nor would they take time off of work to have someone look at it.
Amateur mistake number 5:

That's not their option. It's your option. You get it fixed immediately upon learning that it's not working and YOU tell them when your repairman is going to be at the house fixing it, whether they are there or not. If they don't want somebody there when they are not home, they WILL be there when you tell them when the repairman will be there., you can bet on it.

Quote Quoting inmom
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They said that they would get heaters to take care of it. I have the text messages where I offered heaters to them and they said they would take care of it.
Amateur mistake number 6:

NEVER rely on a tenant to do anything to absolve you of your statutory obligations, no matter what they say.

Quote Quoting inmom
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They also had a dog in the apartment when the lease said no pets.
Amateur mistake number 7:

You should have served the pay or quit notice for that the minute you discovered that they breached the lease by having the dog there.

Quote Quoting inmom
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Now they are saying that they could break the lease (3 months remaining) and do not have to pay those bills that I could take it out of their security deposit.
Amateur mistake number 8:

Never take legal advice from the enemy.

Quote Quoting inmom
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Security deposit was $400
Amateur mistake number 9:

Always get a security deposit of 1 1/2 months rent (at least).

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the bills are $512 without the $1200 for the 3 remaining months on the lease.
As already pointed out you must mitigate your damages by rerenting as soon as reasonable possible and then they will only owe you for the interval from the move out date to the rerent date. If you don't mitigate they can use that against you in court along with claiming that the defective heater was constructive eviction.

Quote Quoting inmom
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BTW, they moved back with parents as they could not afford. Lost jobs because they were arrested for selling pills.
Irrelevant with regard to your decision to sue them or not.

Although with the heater issue a judge might rule that they had good reason to move out. In case you are wondering, there is probably something in your state's landlord tenant statutes that says you can't accept a tenant's waiver of your own obligations.

You might just want to consider accepting this fiasco and consider it a life lesson from the school of hard knocks and learn from your mistakes if you plan on continuing to own the rental.

Meantime, here is the Indiana landlord tenant statute in case you haven't bothered to study it yet:

http://law.justia.com/codes/indiana/...32/article-31/