Below are two pictures of what you may encounter with LED
ribbon cable problems. There are other problems that could be caused by
bad connections (blank screen, solid red screen, etc), but these are the
most common.

Constant horizontal lines across the display

Partial horizontal lines and random noise
To fix, first you're going to need to open up your Virtual Boy system. Click HERE for instructions how. You don't need to completely disassemble, just enough to get to the LED bar displays. Once apart, follow these instructions:

This is what you need to get to. Unscrew
the two small phillips screws holding the LED PCB to the plastic case (DON'T
unscrew the star screws or you may mess up the alignment). Pull the cable
straight out of the socket on the motherboard.

This is what it will look like after removed.

Here is the display removed.

Take one or both displays and lay them on a piece of aluminum foil or baking
pan with the clear plastic cover and cable pointing up. Preheat the oven
to 180-200 degrees F.

Once the oven is preheated, put the displays in until the cables soften
up (wait until the cables lay pretty much flat). There's no need to cook
them excessively long (you don't want to melt anything), a couple minutes
should be plenty of time.

Immediately after removing the displays from the oven, flip them over and
rub the back of the cables to the PCB to ensure a good bond.

After making sure the cable is connected to the PCB well, I suggest reinforcing
the cable with a piece of tape. I cut thin strips of clear packing tape
as it resists stretching and the adhesive is good, but other tapes probably
work as well.

Then wrap the tape around the display. Be sure to tape it as shown so the
tape can't come loose since it will be screwed up against the plastic housing.

And then of course reinstall the display reverse of the removal.
A little history about this problem. I don't believe this problem is necessarily related to abuse. The cables are very light and nothing is loose enough that would get knocked free if subjected to shock (I'm not saying it's okay to beat up the system... there are other parts that won't take the abuse). I saw this problem with my personal system (which I take very good care of) several years ago and decided to attempt to fix it. I tried several methods, but this one I've found to work best. Another interesting fact... I had a BRAND NEW Virtual Boy system a while ago... BOTH displays had problems related to the cables. I believe the problem is actually caused more by the IPD adjustment than anything. The brand new system had the IPD adjustment turned in, which caused the display cables to be pushed outward, detaching it from the rubber glue and of course causing glitchy displays (see pic below). So, it may be a good idea to turn your IPD outward if you plan on storing it for a while. Note: The rubber glue isn't important to the proper function of the display, it's merely a reinforcement.

Notice the rubber is seperated from
the cable.

Compared to another display
where the rubber is still attached.
After you put it back together, you might want to put in standard phillips screws to make it easier to put together and so you can open it again if you want, and you should check the alignment by inserting a game and pressing Left, B, Down, A, Up on the right D-Pad.