@bretthaskett first we will need to know the exact model for your Magnavox. Then it would be great to actually see the boards. Post some good pictures of those with your Question. That will allow us to see what you see. Here is the guide for that Adding images to an existing question
Next we will need to know how it shuts off. It is important to know if it totally turns the TV off (power LED and all) and if you can immediately restart your TV. Details are fairly important with remoted repairs. We are blind and deaf without you, you are our eyes and ears.
As a generic answer, since we do not have the details yet, would be that this is a bad power board, or a bad main board. If it turn off after the Splash screen, it is possible that your TV fails the power on self test and turns off to protect itself. You will need a multimeter to check a few things once we have more details.
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