It certainly may be the case that your screen is decrepit with age. However, before you settle on that, try a couple things.
Open the battery cover and observe the small screws a at the lower corners of the compartment (not the tri-wing). The screw on the left adjusts the top screen, and the one on the right adjusts the bottom screen. Using a 00 Phillips screwdriver, you can adjust the screen brightness and tracking.
Another common culprit in top screens going blank is the connection between the top screen and the motherboard. If the connector isn't seated just right, the screen will not work properly (and in the DSi and DSi XL, the entire console will not work). To get to the connector, you have to open the back of the device (requires a tri-wing screwdriver). The connection is on the underside of the motherboard, so you will have to remove most of the connections a screws on the motherboard in order to access the connector. Use a pair of tweezers to ensure the cable is fully inserted.
It could also be that the cable connecting the screen and the motherboard is torn or faulty, and in this case I would give the same diagnosis as a weary screen.
Best of Luck, let us know how this resolves.