This Xbox Hard Drive Replacement Guide mentions nothing about the ATA security employed by the original Xbox’s firmware that prevents easily swapping drives between different consoles. Without first unlocking and relocking the HDD to the new console’s motherboard (HDDKey), you cannot just swap HDDs from one to another.
Is it an original Xbox, Xbox 360 or the latest Xbox One? Very poor naming of the consoles on Microsoft’s part. Most used to call the original 2001 released Xbox the Xbox 1 after the Xbox 360 was released and now there’s the Xbox One (spelled out) and Xbox One S and Xbox One X. (Argh!!)
Power brick (external power supply) was on the Xbox 360 or Xbox One not the original Xbox. The original Xbox’s power supply was self-contained.
NO, you cannot.