Fry's Electronics newspaper ad (Sat) is featuring an Asus 24x DvD-RW drive for $18.99.
Plan on picking that one up & also take Magnus's advice & remove the disabled drive and disassemble it. (I believe 4 screws hold the cover on.) One way or another, you should be able to work the tray open (eg, manually manipulating the tray gear mechanism) or better yet thru using the emergency eject access hole. In the case of the access hole, the wire being used is not a pure in line insert but must be inserted at a slight angle to engage the internal releasing lever. With the cover off, you might better be able to see what's going on.
PS: If it just the tray belt that's bad, these can be ordered (they're pretty much a standard size) then replaced. I had to just recently replace the tray belts on two of my Plextor DvD-RW drives.