Xbox 360 Hard Drive Compatibility: Old Drives Don't Fit Xbox 360 S (Kinect Bundle)
No, you cannot put an old Xbox 360 hard drive into the Xbox 360 S (the "Kinect 360" slim model).
Why?
Different interfaces: Original 360 (Fat) uses a proprietary PATA (parallel ATA) connector in a custom enclosure. Xbox 360 S uses standard 2.5" SATA (same as laptops).
Internal design: The 360 S has an internal SATA bay; the drive is not meant to be user-swappable easily (requires opening the case).
What You Can Do
Upgrade the internal drive: Buy a compatible 2.5" SATA HDD/SSD, open the 360 S, swap it. (Voids warranty if seal broken).
Use external USB storage: Plug a USB HDD/flash drive (up to 2TB, formatted by Xbox) for games, profiles, saves. Easiest, no opening.
Always back up saves & profile before any hardware change.