Someone gave me a free Insignia NS-32LCD today (Dynex 1st cousin), that powered on OK, but there was no picture.
Found the problem in a couple of hours. The power supply board has 3 fuses and the fuse feeding the 24 volt output connector was blown.
It was a miniature 'pica' type fuse that is soldered directly onto the board.
Although I did not have to trouble shoot any further, I understand that the inverter board is fused as well.
While you're at it, check for and replace any faulty (e.g. leaking, bulging tops) electrolytic capacitors as well.
However, in this case, the only problem I found was the bad fuse (which is a $ .50 part).