I know I posted this quite a long time ago, but it took me several months to clear off all the titles ahead of the problematic one and then I forgot about this post for awhile. I did solve the problem, so I thought I should post the outcome.
Eventually, I removed everything other than the title that wouldn't play and as Wajo suspected, it didn't make any difference - the title would still not play. I tried a soft and hard boot a couple of times each and that didn't work either. However, I did manage to solve the problem by accident. One day I walked away from the unit with the title that wouldn't play in Edit mode and the usual 00 displayed on the timeline - despite the fact that this was a program that ran for several hours. I think I had forgotten that I left it in Edit mode and went away to do something else. When I came back, about 10 to 15 minutes later, to my amazement, the title was playing! At that point I was able to divide several minutes off the front and delete the starting portion. Once that was done I could edit the rest of it - which was what I wanted.
So if anyone else ever runs into this problem - frozen title that won't play - try going into Edit, pressing Play and then leave it like that for a long time. My guess is that the start point was lost and that even though it looked as if the unit was doing nothing it was actually searching the hard drive until it found it.
Now if I can only solve the noise that the hard drive makes - like a small airplane. It was very quiet when I first bought it, but at some point along the way it developed this noise. I opened the case at one point and determined that it is the hard drive whirring away. I don't think I've ever heard a computer hard drive do that. Maybe I should try Wajo's hard drive replacement trick. It's just that everything has been working for many months since the frozen title happened without incident, so I hate to try it in case it doesn't work again.