Even though the physical components (heads, platters, preamp, voice coil, motor) may be identical, a SATA and PATA drive will differ in their firmware. This firmware resides in a hidden System Area on the platters. Therefore a SATA/PATA board swap won't work.
If the drive spins up but clicks, this would suggest that the board is OK. Instead the fault is most likely an internal one, ie heads or media.