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An easy fix? No!
However the problem given the explaination is most likely in the power supply or the power button, test the power button for voltage in, you can also tes the power supply voltage. There should also be a fuse on the board to check.
That does in fact sound like a bad power switch, you would need to remove the outer power button and then press if the problem is still there then the internal switch is bad, this switch is soldered right onto the board, to replace one would first need to locate a switch then desolder and solder a new one in place for a shop to repair it you will be looking at around $100 or so including parts and labor possibly even more, most places you will find will not even provide a board level repair as most will only replace the board which again is not available. It is actually better to replace it and could cost less to replace as well.
Now if less then 1 year old then the item should still be covered under the manufactures warranty in which case you would simply only need to call them for repair/replacement.
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