Looking at your pic, that appears to be a diode that blew. If you heard a "pop" noise, that is a diode for sure. I hate to say it, but that is not easily repairable, and may not be the only problem on the board.
Instead of repairing the board, you might try to replace it with a known good board (same exact make / model of drive)
The board itself comes off easily on most drives.
This is a better alternative to paying a data recovery service.
A quick search on ebay showed lots of circuit boards for drives,...
What kind of drive is it?