The symptoms almost sound like the BAD CAPS problems. To learn more type BAD CAPS on google.
Now type SAMSUNG BAD CAPS to learn about BAD CAPS and HDTVs. Yes I know but the discussions about the SAMSUNGS give you a clue about your set.
If it's out of warranty and they won't fix it, read the discussions about cost to repair.
My 3 year old LCD comes on by itself sometimes and also will not turn on with the remote. When you do turn it on with the side button, the volume goes instantly to max and you cant do any other funtions. Almost like it the volume button was stuck on.