Any TV with a remote has the internal remote control circuit powered all the time (red LED indicator on). When triggered, it closes a relay or solid state switch that is usually on the power board (red LED off). The power switch will trigger that as well as a signal from the remote. Therefore the likely cause would be the power board, but may be the remote receiver which is normally separate.
At any rate, it requires opening up the TV and making some tests. But, without service info it will amount to parts jockeying to find the right part - and it may be just a bad connection.