I recently encountered a problem where Ubuntu would boot in Low Graphics Mode and it wouldn't log in for no apparent reason. Logs showed no errors, older kernel did not change a thing. The system showed absolutely no other symptoms of a problem. After a lot of testing and investigation it turned out that the disk was completely full. That caused the aforementioned behaviour. If you ever run into this, make sure to check your disk usage from a console:
If it turns out that your disk is full, free up some space and reboot your machine - all should return to normal afterwards.
This may sound like a really rare problem, however with the recent proliferation of SSDs, people end up buying small drives due to their lower price tags. That was my case as well. Those usually come in 60-120GB sizes and that's not a lot. With current high definition media formats, a disk of that size can be filled in no time.