I'm sorry to hear that, and to give you the bad news on these sets. Unfortunately the way they're built are more to make them thin and streamlined, and almost all of the parts are outsourced to the lowest priced manufacturers in China. It's what's become of almost all American electronics unfortunately.
This means that the power supply in the TV is locked up and not powering up properly. This is repairable, but whether or not the cost of repairs is worth it is another matter entirely.
The power supply board needs to be replaced inside the set, as the humming that you're hearing is a shot in the transformer's secondary output which provides all of the voltages to operate the TV.
The average cost to have the board replaced in this set is around $150 parts and labor, and considering the set can be replaced for around $200-$225 for a brand new TV with Warranty, I would recommend against repairing this TV. I know this is not the answer you hoped for today, but the TV does indeed require service, and it is not a cost effective repair on a TV of this size.
I would consider putting that same money towards an LG or Toshiba as they tend to have better reliability from what I've seen.
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