Right.
Loss of time / date would imply a battery failure. This is usually (but not always) a CR2032 “button battery,” dead easy to replace if so. It’s not generally indicative of catastrophic failure.
Swapping XP hard drives between PCs might work. It also might explode in spectacular fashion. A ‘known good’ HDD blue-screening when transplanted into another tells you nothing.
The hard drive isn’t “tied to the motherboard,” however for an OEM install you’ll need branded media to reinstall using the serial number on the sticker on the case. There are ways around this.
But to be honest, I wouldn’t bother. Windows XP is a fifteen year old OS which went out of support years ago and in 2017 I’d spend less time working on an XP system than I have on typing this reply. You can pick up a Windows 7 licence now for about £15.