Is the old hard drive not working at all? If it does still work, reinstall it and retrieve your license key using ProduKey. Write it down.
If you do not have access to the old drive, look in your BIOS settings and see if the key is in there somewhere.
If you still cannot find the key in BIOS, during the Windows Vista installation process, leave the key field blank and click next. Once the OS is installed, it may automatically activate by identifying itself with its hardware when the PC goes online.