Hi John,
are you still using Beta 1 or did you update to Beta 2?.
If you are using Ubuntu Mate 15.04 Beta 1 or 2, you most likely won't be able to get the network running in recovery mode due to the fact it is buggy and doesn't activate the network even when you select it in the recovery menu and that is using a network cable!.
(That may have changed recently as I have done several updates and have not used the recovery menu in a while!)
Anyway, try the following, boot into recovery mode and activate "Network" (using a network cable not WiFi) and then go to "root" and enter the following commands:
sudo dpkg --configure -a
then:
sudo apt-get update && sudo apt-get dist-upgrade -f
You can also try this one too:
sudo apt-get update && sudo apt-get install -f
which may or may not fix a broken install!.
Restart with Ctrl + Alt + Del, do not click on resume!.
Another thing that I can think of, when you were updating; did you get asked to replace files but didn't?.
I know we have been through all of this before but its really all I have!. Your other option is to drop down to a stable version of Ubuntu Mate as your PC doesn't seem to like the dev version and upgrade when 15.04 goes stable!.
Does your PC have 2 CD/DVD drives?, if so, take them both out and check that the jumpers in 1 is set to "Master" and the other to "Slave", it is also important to check and see if one of them has the jumper in "CSel" (Cable Select) because if it is, that can cause random crashes on PC's!.
The only other thing I can think of is that you go into your system BIOS and reset it to factory default:
Hope it helps!. 