Video and NIC are not a problem, mainboard can be a problem (if a different HAL is used it will not work), hard drive controller can be worked around. If this was a disaster recovery forget about it, since this it is not this should work. I say should because not all controller drivers work the same.
Install the new driver on the old system. After the install of the driver you have to go into the registry to make sure the START value is set at 0. Now with the driver installed and configured to startup do the backup, and the restored system should start up correctly.