I concur, it's best to install that SATA drive into a new or a known working box and attempt a data recovery that way.
That being said, there is a chance that the filesystem on that drive is corrupted enough to cause the error and reboot issue you described as well.
If this is the case you may need to connect that SATA drive up to a third party controller card instead of the onboard SATA.
Some of the higher end boards come with a third party SATA, like those from Promise or Silicon Image, on the motherboard as well, this should work as a sub to a PCI expansion card as well.
Another option is to use a data recovery tool, I personally have used R Studio and I swear by it