I am no TV expert, but it sounds like you're on the right track. The click is just a one time click? Or repeating?
One time clicks are usual relays which is just a switch basically. Repeat clicking could be an issue (either a fault relay, or inductor usually) But if it doesn't power on, replacing the power board sounds like a reasonable next step.
There is a more thorough [[TV Will Not Turn On|troubleshooting page for TV Will Not Turn On]] that may also be of use here.