When I turn on my Samsung LNT4669 it seems to make a clicking noise a few times, and goes on and off, on and off, a number of times (sometimes as long as 20 seconds) before finally turning on.

Got to Samsung's support site and fill out a request:
http://www.samsung.com/us/support/service/request

You will be contacted by your regional repair center. I'm located in Milwaukee, WI and was contacted by a repair center in Elgin, IL, which is 60 miles away.

The regional center said they think it probably is a electrolytic capacitor issues, as multiple models of Samsung LCD's have this issue. They have defective (too low voltage) capacitors which will eventually give out. Unfortunately he said my model was not on the list they have for a free fix. He gave me the number to Samsung's Executive Customer Relations department, which I then called immediately. The woman there checked and found that my model indeed was covered - she updated the Support Request, and instructed me to call back the regional repair center.

I called back the regional repair center (immediately after finsihing with the ECR) and got a different person on the phone, and gave them my ticket number from my original request. He said since ECR updated it stating my model was covered they would fix it for free. If it's not the capacitors that are causing the problem I will be charged a 150$ fee, plus any parts required to fix the TV. I agreed to that since my local TV repair quoted me 200$ to fix the capacitor issue alone.

Today is January 25th, they have me scheduled to have a repair tech come to my place January 7th to do the repair.

You can fix the capacitors yourself for very cheap, maybe 20-30 bucks if you don't have anything: soldering gun/solder/flux/capacitors/etc...

I'd just go through the service request path, get it fixed for free and have a professional do it. Total time for me was 2 minutes for the service request, 10 minutes on phone for regional repair center, 10 minutes for ECR, 5 minutes for regional again. The repair is expected to take 15 minutes - most likely they'll just swap out the entire power supply board rather than the individual capacitors. Basically 1 hour of time to save minimally 150-250 dollars. I bet not many people asking to fix this make 150 bucks an hour...pretty simple math I think.
-Ryan

Replace bad caps in power supply near connector going to main board (where the inputs are) or just replace power supply board p/n: bn44-00166c