I don't know, that is strange. I am at a loss too. Maybe try booting to a Live CD and look around. Also check the /tmp directory and maybe remove some stuff from there.
This might be one that needs the master's help....cpg
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My HDA: Intel(R) Core(TM) i5-3570K CPU @ 3.40GHz on MSI board, 16GB RAM, 1TBx1+2TBx2+4TBx2
That is puzzling.
Take a look at your /var/log directory to see if you have some large log files you can delete. Take a look at /var/log/messages before you delete it to see if there are meaningful messages in there.
You may need to boot from a liveCD in order to fix things. It sounds like things are too hosed to do much at the moment. I suspect that once you clear out enough space, you might be able to reboot and get it running again.
I can't explain the 'out of space' while df shows room on your partitions. Are all your partitions shown on that list? Any of them missing?