Those are the inductors on the +5V supply. There is a risk that the preamp may be damaged, but you have done hundreds of head swaps, so that shouldn't concern you.
The first thing to do is to remove the shorted 5V TVS diode. I recommend flush cutters for this purpose, or you could use a soldering iron if you prefer.
http://www.users.on.net/~fzabkar/HDD/ST ... 5V_TVS.jpgMy TVS diode FAQ lists suitable replacement diodes and sources.
http://www.users.on.net/~fzabkar/HDD/TVS_diode_FAQ.htmlThe next step is to replace the burnt inductors with wire links.
http://www.users.on.net/~fzabkar/HDD/ST ... uctors.jpgAttachment:
wire_links.jpg [ 76.16 KiB | Viewed 8216 times ]
I suggest you use the end of a resistor leg. Bend the leg, tack solder it in place, then trim it to length.
I recommend that you backup the contents of the serial EEPROM before doing anything. I also recommend that you recheck your PCB for short circuits before powering it up again.
That said, if the only problem is the diode and the inductors, then the two wire links should be all you need to do.
Good luck.