Man that's a tough break. I'm sorry. So you're basically saying that the drive mechanism won't take the disc all the way into the system, correct? The simple fact that you had to use tweezers to get a disc out would be enough to make me return the system, because I can tell you, you just barely have to put the disc in mine and it snatches it right into the system and almost immediately pulls up on the Wii channel. Even the Gamecube games go in pretty easily.
Try this. Situate the Wii horiztonally with the rubber bumpers on the bottom face down. Now take your Wii Sports disc and ease it into the opening very slowly and gently. Just basically putting enough pressure on it to move it inward. When it takes the disc, grip it for a split second as the Wii tries to take it in and then let go. Sometimes the gri mechanism gets off a little and that should pull it tight if it has. If this doesn't work, you're going to have to return it either to the store or Nintendo. I know that Nintendo will immediately send you a replacement unit but you have to give them your credit card information in case you fail to return the original broken unit. Might be the only thing you can do. I just got my Xbox 360 back from Microsoft today from being fixed for the SECOND time. If you have any more questions let me know.