I have the exact same problem as this user, but it only freezes under too heavy load, e.g. when I try to run the installer. I have a HP Pavilion 15-aw027no. After trying multiple USB's with no luck, I went on to DVD-RW's. This worked perfectly (almost), no freezing or crashing, but now whenever I try to install, I get this:
[Errno 5] input/output error
Tried a different DVD, same output. I've tried 4 different DVD's, all with no luck. I've tried to run Memtest86+ to test my RAM for errors, but it returned negative. I tried to run sudo fsck -cc /dev/sda6 to test the part of my SSD which I'll be installing Ubuntu onto for bad blocks. It returned almost 300 errors. I then tried to install in the same session, hoping it would avoid the bad blocks, but this didn't seem to be the problem. Errno 5. I tried HP diagnostics (F2 during boot) extensive system test, no errors, even though fsck returned so many errors. I tried again after all this, but I keep getting the same errno 5.
Also, I checked the MD5SUMS, SHA1SUMS and SHA256SUMS of the ISO I was using, and they all matched the ones on the website.
UPDATE:
Installation with bootable USB worked after adding nomodeset to the grub entry, but now nomodeset is present in the installed version of Ubuntu (the one on my internal drive). Whenever I try to remove nomodeset from the grub entry, Ubuntu becomes very unstable and freezes. The net time I reboot the system, I get this screen
I then booted from my bootable USB, executed sudo fsck -cc /dev/sda6 and got this output. The problem now is, I'm back to where I started. nomodeset is enabled again, and when I try to remove it again, same thing happens.
UPDATE 2:
Well, I didn't quite solve the problem, but I found the cause. I've been trying to install the fglrx-drivers, but I eventually found out that they aren't supported after ubuntu 14.04, so I went on and installed that. This time it didn't run in basic video mode, but it kept being unstable, and crashed all the time, so I tried to install fglrx, but no luck. I couldn't log in, I was stuck in a login-loop, where it would keep logging me out (this happened with the drivers downloaded form AMD's website too), so I pressed ctrl + alt + f1 and logged in through the shell. By looking in some log files, and searching the web, I found out that my GPU (which is a Radeon R7 M340) isn't supported by fglrx, so I went on and uninstalled it, and after that, I was able to log in again. The open source drivers work OK, but if I try to play a youtube video, it will lag AF. I think I'll just avoid AMD cards from now on.