(I Am Not Karsten.)
On Windows boxes it's best to do a fresh install on moving to new hardware due to the various drivers that may be different between the machines. I would think the same would apply to Debian as well.
[link|http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&oe=utf-8&threadm=20030528053014%2472ab%40gated-at.bofh.it&rnum=8&prev=/groups%3Fhl%3Den%26lr%3D%26ie%3DUTF-8%26oe%3Dutf-8%26q%3DTransferring%2BLinux%2Binstallation%2Bto%2Bnew%2Bhardware%26sa%3DN%26tab%3Dwg|This] post in Google's Usenet cache discusses a similar situation - perhaps it'll be helpful.
GL!
Cheers,
Scott.