Double jeopardy only applies to criminal matters. First of all, actions for nonpayment of rent and seeking eviction are separate and apart from actions which determine liability for rent owed pursuant to your lease/contract with the landlord. The first action was likely for the purpose of evicting you and re-taking possession of the property. Your landlord would be within his/her rights to sue you for any unpaid rent owed pursuant to your lease for the duration you lived there and did not pay rent.
DISCLAIMER: Brandy A. Peeples is licensed to practice law in the State of Maryland. This answer is being provided for informational purposes only and the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship. For legal advice relating to your specific situation, I strongly urge you to consult with an attorney in your area. NO COMMUNICATIONS WITH ME ARE TO BE CONSTRUED AS ARISING FROM AN ATTORNEY-CLIENT RELATIONSHIP AND NO ATTORNEY-CLIENT RELATIONSHIP WILL BE ESTABLISHED WITH ME UNLESS I HAVE EXPRESSLY AGREED TO UNDERTAKE YOUR REPRESENTATION, WHICH INCLUDES THE EXECUTION OF A WRITTEN AGREEMENT OF RETAINER.
You need to get the prior judgment entered for possession and see what it says. An L/T action is generally for possession not money. If the order specifically precludes the recovery of the rent, then you have a leg to stand on. If it is silent, probably not.