Convergence = the joining together of the 3 colors making up the picture
Here is a picture of a Convergence mis-alignment
Replace both convergence ICs + any burnt up resistors + any blown fuses = repair cost $250-350 or repair it yourself for about $30 and a few hours of time. Repairing requires tools, soldering and disassembly skills.
All CRT rear projections have 3 picture tubes - red, green, and blue.
Each picture tube has an electromagnet (yoke) that pulls the beams horizontally or vertically. Therefore, there are 6 convergence amplifiers. One for each color, vertical and horizontal. Any one of these amps can fail independently, or whole sections can fail. Depending on the design of the TV, almost all use an IC (integrated circuit or "chip"). These have a part number beginning with STK (ie stk392-110 most common *see pic below) and run very hot, and fail regularly (5-8 years). Most STK designs have 3 amps per IC, giving you 2 ICs to run the convergence. Many manufacturers will have all 3 vertical amps on one, horizontal on the other. Others will have both the red amps on one, the blue on the other, and the green will be split between the two ICs.
The best way to diagnose is to enter the convergence alignment for your TV. Some TV's will have an auto alignment, others will let you adjust the colors yourself. The auto align is hard to troubleshoot because you cannot tell which will not move. If auto align does not work, you have some sort of failure or malfunction. In a manual alignment, you can see which colors will move and in which directions (vertical or horizontal). Using this deduction, you can see which amps have failed and replace accordingly. Red and Blue are typically adjustable, while green is left to factory alignment and not user adjustable. Try looking at the picture with something familiar on the screen. Try to have words or letters around the edges. You can usually see which colors are straight and where they belong, and which colors are out of place. If every color is off in both directions, this is a good indication that there is no power at all. The amps run off + and - 24 volts, and usually have 2 fuses for each power supply line. If everything is off, these fuses probably blew when one or both of the ICs shorted out. *RCA customers see below* Each convergence amp has some resistors that set up the amplifiers gain. Typically and input resistor (small like 1.5 ohm 1 watt) and a feedback resistor (larger like 150 ohm). Its quite common for the smaller value input resistors to blow out, so check them before you replace everything. They are typically right by the ICs (largest heatsinks in the tv) and most of them you can see if they're burnt up. Unhook the yokes (mark them if unmarked) and then you can OHM out the resistors to see if they are opened up. Replace any possibly bad resistors, sometimes they check good but look damaged = replace them! Some TVs will just be dead or go into shutdown. If the + or - 24volt fuses are blown, suspect the ICs and replace them both.
This is kind of tricky, as these ICs usually have 18 pins on each of them. Find all your bad parts, remove them and replace with good ones. The fuses and resistors are pretty straight forward. The ICs are harder. They are mounted to the heatsinks and depending on the make and model, they can be hard to get out. They are thermally bonded to the heatsink with heat sink compound or paste. If it is dry, replace the paste with new stuff. Make sure to get a nice, even, and thin layer on there to give a good heat transfer. The trick to the ICs is to make sure all your pins are straight before you install them. Start at one end and slowly work the IC and get each pin to pop into the hole. Once you solder in all the bad parts, the TV should be able to kick back on and run. At this point, its good to center the colors up in the customer mode. If you want to take it further, get the service manual for that TV and go into service mode and do the full re-alignment. This can backfire so get the manual or make sure you know what your doing as you might accidentally erase all the data.
*stk392-110 = the most common IC. Almost all look just like this
Convergence is a very common failure and can be repaired by someone with a little soldering know how and some time to dedicate. Its quite complex, and every make and model are different. Let me know if you have any specific questions for your product and I can help you get the job done. Remember to have patience, good luck!
*RCA typically uses no ICs, and the convergence power board blows out (older models - wood cabinet) OR a small fuse blows out because of solder connections on the flyback transformer (newer models - plastic cabinet) and just needs resoldering and a new fuse.