Back rent judgments, broken leases and so on can follow you for a long time, but 10 years ago?!?
Unless the amount of the rent you didn't pay is huge, it shouldn't be an issue with a rational owner or property manager.
If you can get your current "landlord" to write you a glowing review of your history, that might do the trick. On the other hand, if the owner/manager still doesn't want you with a glowing recommendation based on a 11-year old event, maybe you don't want to be dealing with them.
McKinney has quite a few rentals http://bit.ly/S9FlGK You might want to check on some other places or have someone help you.