RE: Kernel update help.
When I bought the XPS 13 in March 2014, it came with Ubuntu 12.04 LTS. I tried to do the built-in upgrade to 14.04 but it crashed and left the computer unusable.
I then got a USB drive with 14.04 and started the live desktop. A first attempt to install with full features enabled also crashed. A second attempt to install from the USB live desktop with minimal features worked perfectly. I have been using it with that 14.04 LTS install for a year now.
Keep in mind that I have a 2014 model, not 2015 - there may be some differences (WiFi card? Other?). However, if the built-in upgrade doesn't work for you, you may have better luck (as I did) doing a clean install to either 15.04 or 15.10.
As always, please do a full backup before ANY operating system upgrade!