There are few types of failure to my knowledge that cause this.
Circuit Hardware Error
One is known as a CDC error, it's usually caused by a failure in a board within the device itself (Possibly due to a manufacturer fault, over-heating or an electrical surge). What this means in say a laptop is you can actually completely replace the screen but you'd still have the error show if it's using the same chipset.
Screen Error
Another failure is with the actual display itself, these are usually less common (dead pixels are obviously more common) however if a fault or damage occurs to a horizontal or vertical line feed it can cause a line across the entire screen, it might be only one colour being predominant or no colour at all (black). In those instances the screen would have to be replaced if you don't want a line, or sent back on warranty as suggested.
Transient Media error
Thirdly there is the less likely one which involves the medium of transition (What cable you plug in the back), if you are using say a HDMI cable you'll find that there are many potentials that for instance HDMI uses and encoded format for data transmission (Designed originally as part of DRM to reduce DVD copies via feed, although DVD-RW kind of undermined it overall) If the encoding is malformed you'll likely not receive an image at all, or in cases where you use sound through HDMI connection too you might not have sound. This fault is often caused by the software and/or drivers (damaged cables can also cause this problem), however it wouldn't create a single line across the screen (I'm only identifying it to generalise the various problems and where they usually reside)
Your problem exists in the first two (one or other), there is no "Wrap it in a towel", "Stand on your head" or "Incant in Latin that Bluescreens are a messenger from the Heavens" fix for this. It's simply a failure at a hardware level that can only be fixed by the company that produced the product or one of it's associate outlets. (You can possibly get it fixed for cheaper than buying a new one, however it will likely be shipped by freight for cheap, which usually means sitting in a dock for months before it even gets to the country of origin to be fixed and then having to take the return journey. If you are lucky, you can possibly find out that your particular product is prone to this hardware failure in which case the manufacturer might fix the fault for free or even have extended the Warranty, you'll have to search out the product online though to see if that's the case)