Problems with my Xbox 360 starting up?

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In September 07 I bought a second hand Xbox 360. I have had it replaced since then. The first one broke down completely. I got the three red lights. The problem with my current one(which I have had for about a year I guess. I have lost the receipt unfortunately) is that when I turn it on, nearly every time I get a message saying "to play this disc put it in an Xbox 360 console" on a white screen, with other translations of the same message. I find that if I put pressure on the disc drive area of my console, occasionally I can get a disc to play, but this happens very rarely. My Xbox also worked when I had been moving it around a lot, trying to get it open to look inside. This would point to some faulty connection, surely. What, I have no idea. I can not return my Xbox again, not without a receipt, and I do not really want to send it off anywhere to be repaired because I would imagine that would be expensive. Do you have any suggestions?