So, you loaded Win7 and let it do its initial hardware detection/driver choice thing in your desktop, then moved the HD to the old Dell and expected it to work automagically?
I hope you didn't let the authentication routine run, because no matter what you do that copy of Win 7 will never authenticate in the Dell box. If you didn't try to authenticate Win 7, pull the optical drive from your box and put it in the Dell. Reload Win 7 on the Dell with a good optical drive.
I'm supposed to respect my elders, but it's getting harder and harder for me to find one now.