RE: Dell XPS 13 Screen Dimming not working from Keyboard ( F11 and F12 not working as FN keys)
Updating the BIOS and video drivers should help. You mentioned using F11 and F12, other possible things to try, holding down FN and F5 together, or if you are using Windows 8, open the charms bar and under settings click the brightness button.
You can also use the Intel HD Control Panel, try pressing the control, alt and F12 keys together or right click on any blank space on the desktop and choose Intel graphic properties from the drop down menu.
Once the Intel HD Control Panel opens click on the Display box and then click on the color link on the top, and then move the slider bar to the right to increase screen brightness.
Please let me know if you are still unable to reduce or increase the brightness of the display.