Creating a Backup Internal HDD From a Different Computer?

So I'm making a backup HDD for someone's desktop. The plan was to make a duplicate to where if the existing one went bad the backup could just get switched out with the bad one and would have the same OS (windows XP) and all of the files and be ready to go. I loaded up the OS on my desktop on home and took it over to their house and swapped it out with their current HDD on their desktop to transfer some files, which were stored on a flash drive. When I had it switched out I booted it up and got a message along the lines of their being no VGA connection and windows failed to start and gave me the option to start it on safe mode. Is it because the hardware on the desktop I installed the OS on is different than the other person's hardware? What can be done to successfully boot the OS on their computer?