**This solution will fix the problem with the unit powering off shortly after you turn it on**

Take out all of the screws in the back and get it opened up, and you will see the main circuit board which consists of the power supply and amplifier section.  Find the capacitor labeled C914 which is right next to a small transformer and several other electrolytic capacitors.  It should read 470uf 16v 105c on the side, and if it's anything like the one I found it will have a bulged top on it indicating failure.  The capacitors around it will probably have nice flat tops and they shouldn't need replacing at this time.  Grab a soldering iron and carefully remove the failed capacitor.  If you don't feel comfortable doing this task, you may want to hire it out to a geeky friend : ) Go to your local electronics repair shop and buy a new 470uf 16v 105c capacitor.  Panasonic, Nichicon, Rubycon and Nippon Chemicon are good brands of capacitors to buy.  Make sure you get one rated for 105c or else it will fail prematurely.  Also be mindful of polarity when installing the new unit.  The negative side on the board is indicated by white score marks and the capacitor will have a stripe running top to bottom on the negative side.  It may help to use the photos below for reference

Here are some photos of the failed cap in my HT-CT60:

Also touch up any solder joints that look cracked or sunken while you have the board out.  I found many bad solder joints on my board.  This unit was obviously NOT made by Sony since the quality of the parts and engineering is severely lacking.  I've never had to replace capacitors in any Sony products before, and I suspect that this unit is actually made by LG or Samsung and re-branded as Sony.