Hey, see my previous post... Sounds like the Invertor is shot.... not the screen. You don't need to replace the screen if the invertor is bust.
Just replace the faulty part. Here's the part you need:http://cgi.ebay.co.uk/IBM-THINKPAD-T20-14-LCD-INVERTOR-BOARD-IBM1-/170478428568?cmd=ViewItem&pt=UK_Computing_LaptopAccess_RL&hash=item27b14e6198
The invertor converts the battery voltage into the high power voltage needed to power the backlight. It's usually a capacitor that has blown on the invertor circuit board. At £15 for a new LCD Invertor it is a cheap fix