By stupid curiosity, I've connected the FDD power cable to the jumper pins of a SATA drive, and powered on the system. The SATA drive's controller burned out. What now? Can it be replaced, and still be able to read the disc?
Theoretically you may be able to replace the PCB with one from an identical drive. Note that manufacturers sometimes use slightly different boards even in the same model series, so you would really need an identical one.
It's possible but somewhat unlikely that the platters (the actual hard drive) is damaged but even if you succeed I would only do that to read data off the drive and then replace it.
And yes, it is also possible that it's damaged beyond repair.
Yes its possible to replace the PCB and its highly unlikely that your data will not be recoverable. After the change of PCB your SATA drive might function as well as it used to.
I have had the connector my SATA drive burned out and replaced to get back to a full functional hard disk
Though as Michael Stum said that it could be damaged beyond repair