if there is no display at all, ie a black screen with no ghosting of an image, try reseating the no 1 connector, try hard reset. If there is a faint image then its the backlight.. this may be resolved by cleaning connector 1, checking for damage. If it's damaged then you'll be able to replace it if you've got excellent soldering skills and equipment. If no 1 connector seems ok then it's most likely the backlight coil.
google backlight coil 3gs for repair guide if you've got some moderate skills with a soldering iron.. or search some of the answers on this site. there are plenty of people on ebay offering the coil (6r8) for under $5 with free postage, heres one for 99c!!!! backlight coil
or if you're not too confident you can always search the web for someone who does these repairs.. quite common to find now!