It's likely that the hardware of Computer B may not be consistent with the hardware of Computer A. If that's the case, and if the hardware in Computer B is more modern that Computer A, it may not be compatible with Windows XP. Newer hardware is more likely to be compatible with Windows 7, as it's still a relatively recent OS.
I have my doubts that you'll get XP to run in a stable way on modern hardware (other than in a VM). However, you could try checking and enabling legacy settings within the BIOS of Computer B (e.g. Legacy Boot rather than UEFI if available).