My 3DS top screen has been broken as far as I can remember. My brother and I both got 3DS's when they first came out. I'm pretty sure when he realized his top screen was broken he switched them (we got the same color). So I don't know if he did something to cause the screen to do this or anything. The top screen goes dark, but I don't think it's the backlight. It feels like something is loose in the front, like right under the screen cover. I think it might be glue or something, because if you press on the screen even slightly it starts working again and you can feel it like sticking, but if you let go it stops unless you press it just right. It also usually works better if the screen is all the way back.
Unfortunately, I don't think there is any good news about your situation. It sounds to me like the ribbon cable that runs from the display to the motherboard is damaged. Other than the speakers, cameras and display, there isn't anything in the top-half of the 3DS. If pressing on it fixes the problem then it is somehow making an electrical connection that has otherwise been broken.
It is my understanding that the ribbon cable is integrated into the display so you can't simply replace the cable and be done with the problem. Instead, the entire display will be need to be taken out and replaced. Disassembling a 3DS, though, is extremely complex. Repairing this on your own would require special tools, steady hands and a lot (and I mean a LOT) of patience.
Now, regarding the issue with your brother. If both of you received identical 3DSs there is a chance you can catch him red-handed if he broke his 3DS and swapped yours out for his. If you kept your original box, and he didn't, you can find your box and check the serial numbers on it against the serial number on the system.
The serial number on the box should be the same as the one on the bottom of your 3DS. If they are different, then someone switched them out. If you and your brother still live at home, you can take the broken device, your brothers presumed working one, and your box to your parents and prove that your device is the working one.
Of course, this may also prove that your brother has been honest and that somehow your device has been damaged. This may not provide any personal reassurance but at least the integrity of your brother can be restored.