Can you use the controls on the back of the TV to change the input to another source and see if that works.
If it doesn't select the Menu button and see if the menu screen appears. Go to Menu Setup and see if there is a factory reset option or a Firmware update option.
Click on image below to enlarge and view.
If you get a chance to do it, try updating the firmware for the TV.
Here is a link to the page. There is a firmware download link on the page (E50 Firmware Update, the download is approx. 73Mb) and there is also a link there for the download and install instructions.
I have found some information not particular to your model but to Panasonic that there is a firmware fix that solved what is known to cause the problem of starting up and then shutting down with a slow blinking light. Not saying that this is your problem but at this stage it won't hurt to try.
Here is what in part it says:
.......The cause of the problem is due to the uneven distribution of mercury in the led backlight, which when cold, makes the start sequence slow down. The issue is resolved by changing or updating the Firmware package.