Blank screen except for a single horizontal line through the middle of the screen.

Hello

Your TVs vertical swee sction has failed. All CRT based TVs have both vertical and horizontal sweep sections to sweep the picture both in vertical and horizontal direction to display it on the picture tube screen. This process is otherwise called as scanning. If vertical scan section fails, you will see a horizontal line at the middle of the screen and if horizontal scan fails, you will see a vertical line on the middle of the screen.
You have to open your TV to retify this fault, as the fault lies in the internal circuit board. Open it after disconnecting it from the mains wall socket, and locate the vertical output section inside. It is very easy to locate. On opening you can see a coil fitted on the neck of the picture tube, called deflection yoke, and there will be four wires from it goes to the main board. Out of which two of them will be thick, and the other twos will be thin. The thick wires are usually colour coded as red and blue. Just follow the two thin wires. You will reach to a plung in socket to which these four wires together connected. Turn upside down the circuit board, and follow the print track through the print side of the above said two thin wires connection goes. it will go to the vertical output section.
Before doing any thing, first look into the circut board for any loose or bad solderings are there. It is a common fault that this section have loose solderings on it, because most of the components will heat up while working. Repeated heating and cooling, make loose soderings to emerge.
Resolder all the suspected points, as loose solderings will be microscopic,a nd acnnot be detected very easly. We in the service field also will fist do this.
Usually vertical output section is composed of an IC related circuit. Solder all pins of that Ic first and feel the effect. If this does not help, desolder the IC out of the board, will be screwed on to a metal heatsink, go for the same type and number. Replacing the IC will solve your problem.
If you wants any more assistance, feel free to contact me through Fixya. OK.