Do you get any response if you operate the menu button on the remote? Does the menu appear?
If so check that you have the TV connected to the correct input for your signal source.
if not it could well be a software problem. The logo coming up sort of proves the video is working.
Here is a link to the LG support page for your TV.
Scroll down to the Software Upgrade section. There you will find 2 downloads. One is a guide that explains how to implement the firmware update. The other is the firmware file itself. Be aware the the firmware file is about 88MB in size. Since the last firmware update was in 2011 you may not be updating the firmware merely re-installing it as it may have become corrupted.
Double check that the model number of your TV is as you stated, as installing the wrong firmware could render the TV inoperable.
Hopefully this is of some help.