I had upgraded to Ubuntu 13.04 and the backlight stopped working. After I upgraded my graphics driver it now works without any additionally tweaking. I got it from here http://01.org/
As of Linux kernel version "3.11-rc3", backlight control works on all three XPS13 models (L321X, L322X HD, and L322X Full-HD)
I'm experiencing this issue. Backlight shuts off during boot, at some point after disk encryption pw. Backlight keys are working (icon displays) except that light does not actually turn on. Trickery with /sys/ and /proc/ and xbacklight don't help.
I'm running 3.11.10 (Debian wheezy, kernel package linux-image-3.11-0.bpo.2-amd64) on L322X Full-HD (see lshw output at http://pastie.org/private/w7wryjv3ebxcisi8oumhuq). Backlight works fine with 3.9.6 (from linux-image-3.9-0.bpo.1-amd64).
Got kernel update: 3.12.9 (pkg 3.12-0.bpo.1-amd64). Now backlight is not totally of, only set to really really dim. Otherwise the same. Backlight controls still don't work.
Turning "secure boot" off and "load legacy boot" on from BIOS boot settings worked for me. Per https://bugzilla.kernel.org/show_bug.cgi?id=59841 the 3.12 should be fixed already, but apparently it was not, at least not for me. However, the workaround mentioned was applicable.