The BAD CAPS (see google) issue is well known and this is the classic symptom. Continued use can result in a dead set that the simple fix or repair won't help.
Many of these are fixed for free when you call it in and ask if you can have the one time free fix for bad caps.
Some time ago, our model LNT4061FX/AA (version CN06) started clicking on and off a few seconds before staying on. It's gradually gotten worse, to the point it cycles & clicks for SEVERAL MINUTES before it turns on. I've seen some postings and forums from other Samsung TV owners that this is a common problem with several Samsung models....something related to blown or faulty capacitors.
Has this model been recalled?
What will Samsung do to fix this problem?