A competent DIY-er should be able to recover the data for $0. Only 1 or 2 wire links are needed to repair the bridge PCB.
Otherwise the OP can install the drive inside his PC and recover the data with a 4Kn aware tool such as DMDE (US$20).
http://dmde.com/In the unlikely event that the HDD PCB is not serviceable, the following company will provide a replacement PCB plus firmware transfer for US$50:
http://www.hdd-parts.com/@rogfanther, I'm aware that the OP did not state that he tested the TVS diodes. However, the nature of the damage to Q3 suggests that the 12V TVS diode was shorted by the overvoltage from the 19V (?) laptop adapter. This transistor would be rated well above 19V, probably 30V or 40V, so an overvoltage, per se, would not have been responsible for its failure. In other words, Q3 was killed by the TVS diode, not by the adapter.
Assuming that the the JMicron bridge IC (JMS577) is powered by the onboard 5V regulator (U4) rather than the USB port, and since the bridge's LED is flashing, this means that the 5V supply was not damaged. This in turn suggests that the HDD's 5V TVS diode would have been OK.
For the benefit of the wider audience ...
JMS577, JMicron, USB3.0 to SATA III enhanced controller
FR9886D, fitipower, 4.5V - 23Vin, 2.5A, 340KHz Synchronous Step-Down DC/DC Converter:
www.fitipower.com/file/image/Image/pdf/ ... N-2012.pdfGD25D05BT, GigaDevice, SPI serial flash memory, 512Kbit, 2.7V - 3.6V, SOP8:
http://www.gigadevice.com/product/downl ... cale=en_US