Hey there, imortal!
I'd second what @jsmithepa mentioned about checking the S.M.A.R.T. attributes of the drive by running it's brand-specific diagnostic tool from the manufacturer. If you cannot find it on their website, you can refer to this thread for some third-party suggestions:
http://www.tomshardware.co.uk/forum/282651-32-best-diagnostic-testing-utility
If the connector is broken, then I'd recommend you to back up your data somewhere else and consider replacing the HDD.
It's possible that the drive is underpowered from the PSU's side, but it could also be the hard drive itself.
That's why I think it's best to check up on its health by running the tests.
In case you want to check up on the PSU's voltages, you can check this guide as well: http://www.howtogeek.com/172933/how-can-i-test-my-computers-power-supply/
However, I wouldn't recommend doing this by yourself, especially if one of the connectors is broken.
Keep us posted with the results, though. Good luck!
SuperSoph_WD