Mid 2012 MacBook Pro, reinstallation of operating system fails

About a week ago, while I was browsing the internet, my mid-2012 MacBook Pro (running an outdated version of MacOS Mojave) grew slow, then completely unresponsive.

It had been running a little slower for a while, but I assumed that was from all the Safari windows+tabs I had on it, plus the storage being a little over halfway full.

I thought it would be fine once I restarted it. It wouldn’t let me click on anything whatsoever, so I had to force it to shut down.

When I next restarted it, it booted extremely slowly: 30-40 minutes before it even showed the login screen. After I logged in, it continued to be unresponsive for the next 1-2 hours while I tried to get it to perform the simplest of tasks without much luck: I only just managed to force quit Safari and another app that tried to open upon login. I wanted to run the virus program, in case one of the sites I visited may have given it a virus?—but the application window never loaded. 

I had to force it to shut off again. 

Since then, I’ve tried:

1: Safe boot. Problem persisted. Still unresponsive and wouldn’t load any apps. 

2: Reinstalling the operating system:

a) Command-R upon startup. The download part of it works, but when it tries to remove the previous system, it fails. I have tried this three times, by now. 

b) Option-Command-R. Fails: error message 1007F. Tried twice, both before and after:

3: Zapping the PRAM/NVRAM.

4: Resetting the SMC.

5: Apple diagnostics. (No issues, it says…)

After the NVRAM and SMC resets, safe boot no longer works: when I try to safe boot now, there’s only a white screen, then a flashing folder icon with a question mark on it. 

Normal boot still hellishly slow, unresponsive. 

I haven’t run Disk Utility yet. The reason for this is because I had neglected to back up my files as of the last few weeks (I know—careless), and I was hoping to preserve them.

What do I do now? Any advice would be highly appreciated.