Question details gives idea that standby power supply board seems cause of problem, tv has two power supplies, one is standby power board as shown in below image and other is main power supply board that is bigger in size.
I guess you sent out main power supply board for repair that did not make any difference on tv problem.
Check out following image of standby power supply board and replace marked capacitors and resistor carefully (5 parts) if you do it yourself or ask local repairman to fix it.
Standby supply output voltage seems lower than requirement of tv and causing start-up problem. These voltage goes to system control chip that controls other functions of tv and standby volts must be stable and accurate to turn On tv properly.
I hope these info will solve your tv issue.