When you go to court the next time, make sure that you have enough money to pay the rent. You just say that your rent was refused, or they lost the check or whatever. The judge right then will go, ok do you have the money right now to pay the rent and all late fees? If you say yes, that is about the only chance you have of winning and eviction case.
Since you have a continuence, try calling the management and offering to pay all late fees and the rent.
You know complex's have to give you notices that you missed your payment as well as 3 day vacate notices. As of January 1st 2006 these 3 day vacate notices have to be placed INSIDE the apartment. Why did you ignore the notices? When you get the 3 day vacate notice you can either pay, leave, or get evicted. If they did none of this, make sure you ask them to show copies of the notices in court.