When you turn the TV on, the picture is a narrow wavy horizontal line for about 1/2 hour. Then the picture goes full screen

The cable is either bad or the cable has not been securely full connected to the input and the output ports can have loose connections and can cause the signal and have horizontal or vertical lines to show up on the TVs screen. The cable will need replacement.

The fact it can achieve full screen when it does work means it can be fixed. One of the components has got tired. A capacitor is a good bet. I would not worry that it's a rear projection TV, this is the sort of fault that would happen on any CRT TV. You should be able to find more specific answers if you look for "vertical scan collapsed" Or Tube TV shows horizontal line.

It sounds that the main power supply section to your TV has the fault. The horizontal thik lines that appears crawling down across the screen should be of video 'HUM'. Have you replaced the main filter capacitor at the power supply section? If not, replace it along with the main rectifier. The AC power is rectifed by a bridge and applied ot this main filter capcitor. It will have a capacitance value between 120 to 350MFD 450VDC. Check this section. Measure the rectifed DC voltage acorss this main filter capacitor. It should be around 350VDC, if your home power supply line is 220VAC. If it is 110AC, this DC voltage will be around 165VDC; and it should be. If rectified DC voltage found lower than the input AC voltage, replace the rectifier bridge. In some sets, this bridge section have four diodes. Some other circuits, a bridge rectifier stalk may be used.

Do you have anything to test it in 1080i? Does it do it on all connections or just one? I had a similar problem with my TV that turned out to be a bad input board. Mine would only display 1080i through the Component connections. All others would show pink and green wavy lines. It cost me around 500 to fix it. Unplug the TV. Remove the back cover for the TV. Using a NON-metal object, or gloves, wiggle the input board (that has all the video connections on it) slowly back and forth and see if the problem comes and goes. You will have to have someone watching for you. If something is loose on that board, the problem should show itself. Narrowing down the problem will probably save you money on repair bills.

you need to go into the settings on the box and turn off letterbox on the picture setting.

Ur tv convergence is dead.U must know how to solders?The 2 STK convergence ICS.and some or all it resistors must change.Tries websites Tv repair World.com,Tvrepairkits.com to repair it ur self.The shop will cost u $300 for parts and labors.

bad cap or cold jonit neens solder

If the set works fine intermittently it may be a loose connection or a bad solder joint. More likely the later. Heat will sometimes make a cold or broken solder joint work. If this changes when you lightly tap on the side of the TV you have a bad connection of sorts inside. These repairs can be expensive unless you find a good repair person.
The syncronizing signals in TV's (keeping the picture locked in) are around the high voltage transformer which is usually the heaviest component attached to the circuit boards. It's stressful over time and I've seen the solder connections crack and become intermittent.

Picture is reduced to a straight horizontal line across the center of the screen.

Good Day, Delano1981;

It may cure the problem but I would suspect the 9 Volt source
CHECK C2P05 100 UFD 16 V OFF PIN 3 OF IC2P01 AND
IC2P01 PART # 270P466020 (9-VOLT REGULATOR). BOTH
ARE ON THE SIGNAL PCB.

This should resolve your TV"s condition.

Good Luck, big IRISH.