The fact that your HDD is preventing your system from booting...turn off all power saving when drive is disconnected and install a rapid image backup app like Macrium Reflect free, make sure it is ready to go...reconnect and boot up let sit for up to a couple of hours...sometimes it comes up slowly, if so quickly make an image. Repeat a few times as it is hit or miss.
Does the drive show up in BIOS?
Boot up a test app like Seatools for DOS (if you can) and test the HDD.
Swap with a known working data cable and power connector.Try recovery apps
. Probably won't work if you can't boot.
Can try to boot from Linux recovery disk called SystemRescueCD
. Superbly powerful. If it will, then use ddrescue to first copy what is undamaged using the -n and a log file and then redo with a try to recover damaged files -r3 and the same log file name (it looks in the log file and skips any files it was already able to recover). I will see if I can locate a script because Linux command line is definitely a bit of a WTF at first.
If one of the drives is an exact match (including firmware version) you can back up the working drive and swap its board onto the nonworking HDD to see if it is a failure on the board responsible and recover data.
Recovery $ervice$ can almost certainly retrieve your data.