I have a sony KV35s36 tv. The picture blinks on and off. What would cause this problem?

Is the picture not as good as it used to be? You probably have a weak picture tube. Sony TVs have an IK (CRT cathode current sense) and if it is at or below a certain threshold (like at warmup or when the CRT is weak) the micro keeps the tube cut off.
You can try and bump up the G2 control (located on the CRT board up a bit to increase the IK.

Also check for bad solder connections at the vertical output IC. If the vertical scan fails the micro will blank the tube to protect it.