In most cases, a boot drive from one type of system will not boot in another type of system. There are all kinds of low-level settings and drivers that will not be compatible. For example, if the old system had a Waxworks 5000 disk controller (yes, that is nonsense) and the new one has a Digistream 73, then the system will not be able to read from the disk to boot.
There are assorted ways to correct these drivers. However, if the old system came with XP installed, this is outside of the licensing agreement with Microsoft and should not be done.
If you have an XP distribution disc and license, you can try booting to the distribution disc and choosing a Repair install. You would do better to do a re-install. You would do even better to buy a new, larger, faster drive if your budget allows.