The picture loss with audio is usually a sign of HDCP (copy protection) from the source. I would suggest unplugging the cable box and trying it again.
I can't explain the humming sound, but would recommend having a service technician take a look at that.
Are you still having the intermittent turn on/and/off?
Several years ago, after research, I bought a 40?Samsung flat panel LCD. I was very happy with it and became a loyal customer. Since then I have bought a DVD player, a 52?LCD and very recently a 32?LCD. Now I am wondering if I did the right thing. The 52?tv (LN-T5265F) was purchased two years ago. I loved the set until about a month ago. It now has an intermittent problem. Sometimes the sound comes on with no picture. When this occurs, there is a humming sound in the right side of the set. The first time it occurred, I turned it off for a couple days. Then it was fine for about a week. The second time, my wife kept turning the set off and on and eventually the picture came on. Looking on the internet, I found several other reports of this problem with Samsung with no solution. I would like to know if this intermittent problem can be fixed.