If you can get an identical hard drive and use the printed circuit board from it to replace your burnt out one, you may be able to recover the data.
If you can't do it yourself it's likely to be quite expensive and no guaranty of success.
If you upload a detailed photo, one of us may be able to help you repair your board. Many times the problem is only a shorted TVS diode, in which case it can simply be removed. Just be absolutely sure your PSU is OK, as you will no longer have any overvoltage protection on the affected supply rail.
When replacing the PCB, you will need to transfer "adaptive" data from patient to donor. These data are often stored in an 8-pin serial EEPROM chip.
These URLs should help you identify the components:
I had the same problem with my hard drive but after doing little bit of research i found these guys, http://www.onepcbsolution.com/ who told me it was possible to get my data back after replacing board on the hard disk..........
Sorry about late in replying but hope this helps to anyone who got their hard disk burned/ smoked..