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If you are looking for an easy, no-cost fix, try removing the keyboard and re-seating the LCD cable. It's possible that a bad/loose/dirty connection is causing the problem. If the ribbon cable-to-motherboard connection is solid and you are bold enough to try removing the LCD panel from the lid, you could re-seat the cable where it plugs into the back side of the display. Now's the time to do a complete inspection of the cable to see if there's any visible tears.
If either of those things don't fix the problem, then you're looking at throwing some $$$ (€€€) at the T20. The ribbon (aka, flex) cable may be the source of the problem. It's about the cheapest thing you can replace. It's also possible that the panel itself is bad or the issue exists on the motherboard and there's nothing you can do short of replacing one or the other.
Here's a link to the Hardware Maintenance Manual for the T2x systems: http://download.lenovo.com/ibmdl/pub/pc ... 2p9631.pdf