Could be a number of things.
Your old machine may have installed custom drivers when XP was being installed (needed for things such as SATA support). If so, the drivers may cause your new machine to throw its hands in the air in confusion.
Alternatively, Dell may have some way of locking the install to their motherboard, because the OEM licence of Windows does not permit the software to be used on any other machine. That would be a handy way of stopping people clone XP disks, but I have no idea whether machine vendors use such methods.
If you got as far as the Windows desktop before things went bad, you could just uninstall the drivers on the Dell machine and then let your new machine prompt you to install what was needed. But if you're crashing before you get that far, I suspect you're stuck.
You could buy an XP licence (or a Windows 7 licence) and install that on your new machine, or you could leave the dark side and embrace the warmth of Linux. (If you like reading config guides a lot.)