I will do my best to help you.
Since you say the computer has been extremely slow since those errors appeared, and since the repair window is taking a lot of time to open, I think there may be a problem with the hard disk.
Both Windows and its repair features are installed on the hard disk, so if there is some kind of a problem with the hard disk, you won't be able to load Windows nor access the repair features.
I am sure the hard disk hasn't failed completely, but will probably need to be un-plugged and re-plugged. So, I suggest doing the following:
1. Turn off your laptop
2. Disconnect the power adapter
3. Turn it over and remove the battery
4. Remove the hard disk compartment to get to the hard disk drive
5. Un-screw several screws to be able to un-plug the hard disk drive
6. Once un-plugged, clean the hard disk area and the connectors from dust. You can just blow the dust away
7. After that, re-plug the hard disk and re-screw the screws
8. Put the bottom cover back and re-connect both the battery and the power adapter
9. Start the laptop normally and see the results
I found a video that demonstrates how to disassemble Samsung NP300E5C laptop:https://www.youtube.com/watch?v=GxyFw4kLbA4
You can see the hard disk and the screws at 04:30.