Recently upgraded ubuntu from 15.10 to 16.04 and I can't get past the purple ubuntu loading screen. After awhile I end up with a black screen and I can't continue from here.
There is not much of a verbose output of any logs or anything I can see but one is: *ERROR* 5.4 Gbps link rate without HBR2/TPS3 support
I tried booting up with a live CD with ubuntu 14.04 on and it works fine.
If you hold your left shift pushed down when GRUB starts (right after the BIOS boot), you should get some boot options. Normally there is a safe mode that might help you out. At least you will get the full boot messages whatever option you choose.
If you have not, please do not forget to make a backup of your data (you can boot your live CD for that).
See this post for a complete recipe for black screen problem solving.
