Your drive's OS is corrupted! You'll likely need to do a few different things here to fix this.
First lets see if you can boot up under Safe Mode. Restart your system and after the bong press and hold the Shift key are you able to get to the desktop now?
If not you'll need to boot up under an external boot drive. Again, when restarting the system after the Bong press the Option key so you can select the other drive. Of course you'll need to have an external drive and have already made it bootable. If you haven't you'll need to visit a friend who has a Mac and setup a USB thumb drive with a copy of OS-X/MacOS you are using on your system How to set up and use an external Mac startup disk & How to set up and use an external Mac startup disk
As an alternative you can also try booting up under the hidden recovery partition About macOS Recovery, check your drive using Disk Utility as well as reinstall your OS. And lastly you can also try using Internet Recovery if your drive is not setup with the recovery partition. I must warn you is't quite slow on most peoples internet connections. So make sure you have a fast link or can leave it connected unintended.
But! Given the fact your system is slow I suspect you have a deeper hardware problem here!
The HD cable in this series has a tendency to breakdown. You might want to visit an Apple Store or Apple authorized service center to have them replace the cable. Apple has been quietly replacing the cable for Free! So its worth getting it replaced. If you can't get to either here is the IFIXIT guide to replace the cable: MacBook Pro 13" Unibody Late 2011 Hard Drive Cable Replacement as for the part I strongly recommend you use this one: MacBook Pro 13" Unibody (Mid 2012) Hard Drive Cable This newer version of the cable is better built.
Ah! I think you're stuck in a tailspin here. Sadly, you still have an OS issue. The problem is you are really over-writing the OS on top so the corrupted driver (or its location on the drive) is not being replaced.
Sadly, you need to scratch the drive and reinstall the OS. But before we do this we still need to make sure if the drive has a bad sector so you don't re-use it. Disk Utility can be misleading as just like a shoe cobbler he can't fix your shoe while you're still in it ;-}
Here we need to use an external bootable drive (not the hidden recovery services either as thats still on the disk). Using Internet recovery would only work if you had a clean unformatted drive. If it see's a GUID partition it will cache to it which then messes things up again.
Of course make a backup before you do anything.
After booting up on the external disk we want to erase the drive using the security Options a single pass will do for us here. The newer versions of Disk Utility are a bit limited. You might find using an older version (older OS) better as it allows you to do a drive integrity test. Or, use a 3rd party tool Like Disk Genius if you have it. The last option is to use the UNIX command line under terminal.
Once the drive is scratched you can then re-install your OS from the OS installer and the test the system. Is it working now? If it is carefully restore your apps and data making sure you don't over-write the OS. That should do it!
If you're brave here's the terminal DISKUTIL commands: Format commands under Term