Funny, I've just recently experienced this with one of my old ones. My tray would keep opening so I just started to forcefully hold it in while trying to start the game from the HDD. Sometimes it would take a few tries to get it to work but it always did. Then it just stopped happening but I suspect I haven't seen the last of it.
It sucks you are having this with a slim but as far as I know Best Buy should let you just swap it out for a new one no questions asked. I have a friend that got a 3 yr. warranty on a fat and he's already exchanged for a console and a controller. From what I remember he said it was quite painless. I'd avoid dealing with MS and the 1-800-4myxbox number at all costs, the worst customer service I've ever had to deal with (several times).
I LOVE paying for Xbox Live! I also love that my love for it pisses off so many people.