I’m new to MATE, but have been using other Ubuntu derivatives for about 4 years. Just done a clean install of 17.04 (amd64 desktop) so it is the only distro on the HDD. My system is a i7-6700 CPU on ASUS H110M-R motherboard with integrated Intel HD graphics and UEFI.
On booting, all I see is wallpaper but no greeter (login dialog). I can login by typing my password (blind - I can not see it). Then I see the desktop wallpaper and the Welcome screen, but there are no panels, menu or icons. I can right-click and get a terminal, or switch to virtual consoles OK.
I removed the HDD and put in in an older 64-bit box with a BIOS, and everything worked as expected. The greeter and panels etc are all visible.
Returning the HDD to the first (problem) box nothing has changed. If I select recovery mode from the GRUB menu, select root mode and type ‘startx’ the desktop loads correctly. I can then ‘su’ to my normal user ID, type ‘sudo startx’ and again the desktop loads correctly.
However, every time I boot normally, the greeter and panels are not visible. I have also tried various combinations of 'mate-panel" with and without ‘—reset’ or ‘–replace’ as well as ‘caja -q’ as suggested in various fora.
Any ideas what else I should try?
Are there any clues as to what’s happening in the boot log (journalctl)? I don’t think it’s a modeset issue, but hesitant to suggest anything else without more info.
Also, once you do get into your system from root and switch to your user and startx, if you just log out, do you then see the greeter panel etc?
@Broken Canoe
I had a quick look at journalctl but couldn’t see anything obviously
wrong. I saved the output for later examination.
I edited the GRUB menu by adding ‘nomodeset’ to the end of the kernel
parameters and that did the job. The greeter and panels are now visible
when booting normally.
On your second point: when I logged out in recovery mode the greeter was
NOT visible.
Thanks for your quick help.
Good to hear you got it working! 
Surprised to see a driver partially failing like that… hopefully you won’t need to use nomodeset permanently!