The backlight is an electroluminescent panel in BL7000, and they can stop working. Check for ~120V AC at the two wires which feed the backlight sheet. If the voltage is present, then the EL material has failed.
It can be purchased either from RS or from china via ebay, or elsewhere.
http://newzealand.rs-online.com/web/search/searchBrowseAction.html?method=getProduct&R=2678784
http://cgi.ebay.com/A6-electroluminescent-panel-sheet-foil-EL-back-light-/380359298268?pt=LH_DefaultDomain_0&hash=item588f2e4cdc
The sheet is cut to size, and the display comes apart easily enough to allow the old backlight sheet to be replaced. Just be patient, take your time and be careful not to get any dust in there!