Repairing startup after defragmenting C

Hello,

I’m explaining my problem (and I apologize for the lengthy message that follows); I started a defragmentation of disk C last night that went smoothly. I then calmly shut down my computer, but when I turned it back on today, a startup repair window opened. The loading lasted about 1 hour, after which the HP recovery manager opened with the following options:

- Microsoft System Restore
- Microsoft Startup Repair
- System Reinstallation
- File Backup Program

I first tried the file backup program thinking about backing them up to an external hard drive, but after a few minutes of creating the list of files, the following error message appeared: "There is currently no disk space available on the system partition for temporary storage during data compression. You must free up space on the system partition to continue the task."

I have no idea how to "free" up space..

I then tried to restore the system but "no restore point has been created on the system drive. To create a restore point, open System Protection." When I open System Protection, the following message appears to which I can only respond with OK: "Your computer is running in a limited diagnostic state. If you use System Restore in this limited state, you will not be able to undo the restoration."

So no system restoration is possible, and the computer restarts, bringing me back to the HP recovery manager. Finally, when I press startup repair, I’m told it's already running, even though I can't access that window.

If I want to close the recovery manager window, the computer restarts and I end up on the same screen. The same screen appears if I try safe mode or last known good configuration with F8. Choosing F8 and repairing the computer brings up a "system recovery options" window where I have to log in, HomeGroupUser$ or my user session. I choose my name since I don’t have the password for HomeGroupUser$. I then have the following options:

- Startup Repair (which I selected, and finally told that if I recently plugged a device into this computer, I need to remove it and restart. However, nothing new on that side!)
- System Restore (no restore point, so impossible)
- System Image Recovery (there isn’t one, so impossible)
- Windows Memory Diagnostics
- Command Prompt
- Recovery Manager (which sends me back to the HP recovery manager)

Thanks to those who took the time to read the entire message, :).

So what should be done to get everything running again WITHOUT losing my files?

Thanks in advance!