I have had this problem twice and both times when I brought them to the TV repair shop, (diferent ones each time) I was told that it was the something in the tube and it would be cheaper to buy a new one.
So, I brought them back home, and with a philips head screw driver, I gently removed the cover on the remote control, removed the batteries and placed them in a safe place until I could find a new TV with a remote control that I could put the batteries in.
It seems to have worked!
I'm sorry, I just could not resist! (being home sick, the meds must have kicked in)
George, if you are able to fix the TV please tell us what you did. I did have this happen to me twice in the past and I now have a Toshiba in my celler with same problem. It almost went to the dump before I read your post.