Whenever possible contact an authorized RTI dealer in your area for support help!
There are a couple of reasons that a T1 or T2+ goes black. I understand that the screen does not light but if the buttons do not light either. The first most obvious reason is the battery is dead, even though it may act like it is charging. Pop the back off and check to see if the battery is slightly bulged. If so, it is for sure finished with its life. Further if the battery is over 2 - 3 years old it is probably done. Replacement batteries are available, but changing them requires more knowledge than just knowing how to use a Philips screw driver. The mother board battery connector is very susceptible to damage, so you must take great caution to hold the white mother board connector down gently on the edge with a small screw driver while you pull the white battery connector out.
Another potential problem area that will cause the screen to go off or become fractal
is that there is an internal screw in the lower left that clamps the keyboard circuit board in place. This is also the ground clamp for the keypad illuminating surface. If this screw was not installed tightly the contact surface underneath will burn off. I have successfully repaired several of these by placing a triple folded small piece of aluminum foil in place of the burned out contact material under the screw and clear plastic illuminating sheet then tighten up the screw.
Only perform repairs if you are qualified to do so J
Master A/V Systems Integrator