I had a LN4051D and had problems with it not turning on right away (having to try multiple times) and when it did come on, sometimes not getting sound.
It got worse over a week, and would eventually just reset over and over (you'd hear the sound of a relay clicking in) until ten minutes later it would finally come up.
The TV was out of warranty, and Samsung wanted $300 just to come and look at it.
A little searching on the net, and I found this:http://www.fixya.com/support/t104842..._power_problem
The problem is four bad 100 microf caps on the power supply board.
Just open the tv (take off the back covere with 21 screws, and the power board with 6 screws), replace it with 4 new caps from Radio Shack, and with some soldering, you're all set in 20 minutes! Cost me under $8 to fix it!
If you have this problem, call into Samsung and complain that they built a tv with bad caps, and they won't fix it for free!