It always gets as far as the Grub menu, but after that, when text appears briefly, the text is sometimes half a screen (which means it's going to boot successfully), and sometimes about two screens (which means it's not going to boot). I show this in these videos I took on 4 September 2015:
Bad: https://www.dropbox.com/s/8d6imetl832rqu2/P9040001%20Unsuccessful%20boot.AVI?dl=0
Bad: https://www.dropbox.com/s/7liksig65l42dtx/P9040002%20Unsuccessful%20boot.AVI?dl=0
Good: https://www.dropbox.com/s/0iz4ejq1my5e1rl/P9040003%20Successful%20boot.AVI?dl=0
When it doesn't boot, the only option is to hold the power button down until it goes off, and try again.
I've found that going into a "recovery mode", followed by "Resume normal boot" increases the odds of booting, but it's no guarantee.
I've booted into "boot-repair-disk" several times, and run the repair application, but it only seems to boot once successfully immediately afterwards, which is what I've just had to do after a kernel update this morning. The boot process, therefore, is even longer than the usual 1 minute 20 seconds. This adds 5 or 10 minutes.
If it's any help, here are the reports uploaded automatically from "boot-repair-disk":
http://paste.ubuntu.com/13851399/
http://paste.ubuntu.com/14059667/
http://paste.ubuntu.com/14059812/
There's no difference between them as far as I can tell.
Thanks.
After all that, it stopped working altogether on 23 January 2016. It turned out that both the Intel W2600CR motherboard, and one of the Intel Xeon E5 2680 processors, had failed.
They were both replaced under warranty, which took just under 6 months. As soon as the computer was returned from the other side of the country to me, and as soon as I had the video card also replaced under warranty (it failed during the couple of days getting my computer ticking over properly again), it was functional again.