I have pretty much the same problem. If you are able to, using the Samsung remote after the tv goes black, press the "source button" on the very top right of the Samsung remote.
If this is the correct fix, the source options should show up on the screen now. Using the arrow directional keys if necessary to place the marker over the intended HDMI source selection; usually HDMI1, then press the middle select button in between the directional arrows. This always brings the screen back up for me so far.
I expect capacitor failure here too, as I was in the electronics industry until recently retired after 39 years.
As a side note, I have never used Warranty Gold on any of my plans; always used the Geek Squad from Best Buy before, so guess it will be a new experience for me.
Never seen GEEK SQUAD do component level repair work in home; they usually just replace the circuit board that contains the suspect failing components. The problem always seems to lead to the capacitors. I actually found inexpensive capacitor replacement kits for many failing tv's out there. Google around. All you'l need is a little common sense, a scewdriver, small solder pencil and a bit of 60/40 solder along with the handful of capacitors to change and make the repair yourself. Failed capacitors are usually easy to locate. The ones that go out are the "Electrolytic" metal type usually round. Telltale sign of failure is usually the top end of the metal can is swelled outward. Others may not show signs of failure and would require more sophisticated equipment to check them, but usually these capacitor kits when you can find them, cover several capacitors that are the likely culprits. Just be sure to observe polarity when you insert into the circuit board! Good Luck!
Hey if this helped, GREAT; if not; DON'T FLAME ME for trying to help. Appliances and Electronics are not made to last anymore; sorry...
BOTTOM LINE if you have a good warranty or service contract with no deductible, let those folks fix it in your home...because that's still bothersome.