problem with 2000 cadillac catera?

My cadillac catera has some kind of problem. It was driving fine one day then just randomly quit moving. I can start it now and it drives fine for about a mile, then it quits moving and none of the gears work, like the transmission went out. Cut it off, let it sit, drive it again, fine for a mile then messes up again. Pushing the gas makes the rpm's go up jsut fine but car doesn't move. There is front end shuddering when it does mess up and if you keep pressing the gas sometimes it will "catch" and go but very slowly with no power and once you slow down it won't go again. Goes great for about a mile, changes gears fine and all, but then it quits again after about a mile. Keeps running, idling fine, just doesn't go. Changing to lower gear or reverse makes no difference. This is a car with a German sealed transmission, the kind you don't have a transmission fluid stick and you can't add any fluid yourself.