I will start describing the problem from scrap. I know you have already done some troubleshooting (eg. disconnecting power), and I know that you are aware that the clicking is not the problem, but I want to go through the full description in the hope of clearing confusion.
The TV is in protect mode. This is a special diagnostic mode that turns on when an incorrect voltage or a short is detected by the TV main circuit board. In protect mode the TV is forced to stand-by, and voltages from CPU are kept off, apart from the low +5V DC that is used to keep the TV in standby. The clicking sound in a protection switch that keeps off the PSU.
The three flashes after connecting power indicate that PSU is good and responding, and that the problem is elsewhere.
To find the real error code hold Input and Menu buttons in front panel at the same time for 5 secs. The TV will return two series of flashes (tens, then pause, then units), which are the error code. Here the procedure:
Here all the error codes for this set:
If you get 12, the PSU and ballast may still need checking.
21: Test XR protect circuit, if good, replace CRT.
22: Check deflection yoke, ballast, PSU and other parts.
23: check alignment circuit and convergence ICs
24: check alignment circuit and convergence ICs
The repair must be done by a person with TV repairing experience. This kind of TV is tested working with iron and multimeter, there is no board swapping with this models.Here the full service manual.