Yeah, that's what usually happens. Though I haven't booted up my Xbox in YEARS, I'm not really sure that would even work anymore. I haven't tried again recently, but I'm far too lazy to go digging around for it <.<
Hey Ghosty, have you tried tapping at the door of the disk drive with your finger after you push eject button? My dad owns about 18 original Xboxes from when we used to have LAN parties at church. This was a prominent problem with some of them.