Ubuntu – Ubuntu Installation over USB and DVD fails

I'm trying to install ubuntu on a new T440p laptop from Lenovo and it always fails for the same reason:

[ 135.292409] SQUASHFS error: sb_bread failed reading block 0x9d7f3
[ 135.292411] SQUASHFS error: Unable to read fragment cache block [275faa28]
[ 135.292413] SQUASHFS error: Unable to read page, block 275faa28, size 23a7

I downloaded the newest Ubuntu (Ubuntu 14.04.1 LTS 64 bit), and now tried with every USB stick that I have, that has over 1GB of space, and no one works!

I checked the .iso file hash with HashCalc, and the hash is ok. I installed the files with Universal-USB-Installer, and that apparently worked too (I actually get the startup screen from Ubuntu, where I have to choose "start ubuntu" or "install ubuntu", etc) – but after 3 different USB sticks, and about 5 attempts, it still completly fails.

The ubuntu load screen simply loads for an eternity, and when I go to a virtual console with CTRL+ALT+F2, it shows the above error getting repeated each couple of seconds.

What can I do to solve this? Burning a CD/DVD is not possible atm, and I only have those three USB sticks to try (and it really doesn't seem like the USB sticks would be the problem).

Any Ideas?

Edit: I managed to burn a DVD now, and I still have the exact same issue! (I re-downloaded the .iso, checked it a second time, and the checksum again, seems to be ok). Even with the DVD, I'm getting:

[ 183.251602] SQUASHFS error: Unable to read fragment cache entry

and

zlib decompression failed, data probably corrupt

How is that possible?