KV-32XBR15
Yes, you should check other parts. The horizontal output transistor is more than likely shorted. Also the flyback could have gone bad. Some SONYs have problems with the horizontal driver transformer which is connected to the base circuit of the horizontal output transistor. If this little transformer has a loose solder connection, it will take out the horizontal output transistor.
This may give you some insight as to where to look for your problem.
Stargazer
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