You can open up the hard drive from the old Xbox and put it in the new xbox. It's not the easiest thing to do, but it's certainly possible.
Have you tried putting that erased 250 GB HDD in an Xbox yet? I would think that the xbox would realize it's been erased and format it and fix the HDD itself? I'm not sure though.
Here's a video tut on transferring old HDD to new xbox:
If you don't have the tools to unscrew it you could always bash it with a hammer and break it open too.
[ame=
https://www.youtube.com/watch?v=l0NhKgRC2tg]YouTube - Transferring an old Xbox 360 Hard drive into the new Slim Xbox 360[/ame]