It says it's a trial?

No, you can play anytime. You do not need to be connected. There is a chance that you just didn't finish downloading the full version or something. Try going back to the marketplace and downloading again. If you've already paid for the game, you will not be charged again.

If the Xbox 360 console in which you originally bought & downloaded the game failed, chances are that the system that you received from repair is not the same one. The problem here is that even though you keep the original Hard Disk Drive, the Digital Rights Media license (one of two) is stored in the console which was used to download the game. (the other DRM license is stored in some XBox Live records and thus it is why you can still play the game while connected to Xbox Live, either Gold or Silver will do ok.)

Now, what you must do to play it off-line is one of two things. The first one you should try is to call 1-800-4-MY-XBOX (you can verify this number in the console instructions books) and tell them what happened, and that you want your DRM license transferred to the console you have at the moment. They will give you instructions on what you need to do. (this option will probably take two weeks while they get to your case and investigate it.)

The second choice is the easier and quicker of the two, but can only be done once every 12 months! For this go and first read here: "support.microsoft.com/kb/963711" then make sure you read this: "www.xbox.com/en-US/support/systemuse/xbox360/licensemigration/faq.htm" and when you are ready go here: "xbox.com/en-US/support/systemuse/xbox360/licensemigration/" I hope this helps in a comprehensive way.