I was having the same problem, I could not get the Ubuntu Mate image to run from my SD card. I tried and successfully ran raspian, ubuntu snappy, even windows IoT from this card on the Raspberry Pi, but not Ubuntu Mate; I tried making the boot SD from an Ubuntu desktop machine and via a Windows install. After reading the above messages, I decided to try one last time with the raspberry pi plugged into the a television via hdmi instead of the hdmi/dvi adapter I was using with an older dvi monitor and it booted right up. For me, it has something to do with the hdmi/dvi adapter and/or monitor. The Ubuntu Mate installer had run when attached to the monitor, just couldn’t see the screen image, I think, because the screen message asked for a reboot when restarted attached to the tv and then ran thru the full install with user creation, etc. So, there is some issue with the Ubuntu Mate video displaying correctly on my monitor via an hdmi cable and hdmi to dvi adapter that wasn’t problem with the other packages.
Note: see now that highsider described the same problem in another topic…My monitor is also an older Dell.