I called them and they wont fix it....they dont know if im trying to put it onto a friends console or what not... but its mine, and if im signed into xbox live, then it recognizes I have the full version game.... but if I dont sign into Xbox live using the internet connection (meaning its upstairs where I do not have one, or if all the ethernet cables are being used) then it will only see them as trial games

Hey all, I tried searching for the answer to this, cannot find it anywhere.
This is what is going on.
I had a Xbox 360 with about 10 games I downloaded from Xbox live arcade. Well I got rid of my 360, had way to many problems, and now six months later, I went out and bought another after I was told they fixed the errors. But here is where my dilemma lies. I was able to re-download my Xbox arcade games, but they only recognize them as the Full Game when I am signed into XBox Live. Is there a way to fix this so I will not have to be signed in for it to recognize my full version games, as I do not always have the internet connection to use.
Thank you