My TV Sony KV-XJ29M50, The picture appears only the bottom half. I've check all the connections on the PCB and the result is good, and I do not see any signs of damage to the capacitor. What's the solution ? ..

vertical setting solution

Check whether there is an audio out RCA type sockets at the rear side of the TVm marked as Audio Out. If so, you can connect these sockets to any exterenal audio amplifier, by connecting Av cable in between devices, and can listen audio from external speakers. Picture of AV cable is shown. Keep free its yellow pins. Use red and white.

Check and replace all electrolytic capacitors at its vertical output section. There will be 5 or 6 numbers. Replace all of them at the same time.

Sir your unit has a loosed or cold solder, remove the back cover of your tv then observe your PCB solder part it is much better if you use a magnifying glass to identify the cold solder, but unplug the unit when removing the back cover if you see this cold solder resolder it but be sure not to connect separated pins, if accidentally connected or solder it may caused much damage to your unit, or you can contact a service technician to do it for you and save you from stress good day and best regards.

The easiest way to identify the Vertical drive IC is to trace the horizontal Yoke coils to the board, the vertical coils to the board must lead to the vertical drive output where the IC is seen normally a inline IC with a heat sink.
Check if the solder joints are weak if so solder and check.

The set has a vertical deflection problem, the vertical ic and a few capacitors will need to be replaced to restore the tv to normal function.

Try connecting the TV directly to a different wall outlet and check. If the issue persists, try power resetting the TV. Turn Off the TV and remove the power plug from the wall outlet for 1 minute and reconnect it and check the operation. If the issue persists, then the TV requires service.

shutdown trouble, some leak capacitor need to be replaced

Problem is with the picture tube.

If I understand you correctly:
The horizontal output transistor in your TV blew.

You replaced it with a BU2520DF.

I'm not sure what you mean by "change to dynamic mode".

Dynamic what?

Usually, horizontal problems in TVs are caused by bad capacitors in either the sync circuit, the driver circuit, the geometry circuit or the output circuit.

When I repsir problems like this I use an oscilliscope to find which stage is not working properly, then start substituting the capacitors in that stage until the problem is solved.

Look for large orange or blue ceramic or polyprop capacitors with bulges or cracks in them.

Look for electrolytic capacitors with bulging tops or shrunk cases.

Check and make sure no resistors are brown, they may be blown.

Use an ohm meter to test low value resistors in circuit.

If you don't have an oscilliscopw, that's about all you can do.