The bad cap models I encountered will come on after awhile. Your symptom sounds like something else.
I don't want to upset you but here's the symptom I look for. It begins with the device clicking once or twice on power up and then later more clicks. In the final stage of failure you might get a puff of smoke and it never comes on. Your symptom does not match bad caps. But you could research this more for pictures of what to look for if you are a repair tech.
Samsung agreed to repair many defective TVs manufactured before 12/31/2008 (see www.samsung.com/capacitorsettlement). However my TV was manufactured in 2010 and is exhibiting exactly the same issues described in this settlement: TV will not turn on, clicking sounds, turning off randomly, etc.
Are there others like me? It is time to start another lawsuit? My TV is a Model #LN32B549P8D.
Frustrated in Seattle