[Arran]

No, you don't need a new flyback, in spite of what rumors have indicated, at least regarding the 1958 models, the flyback transformers seldom fail. However you will have to reattach the cap to the lead, it's most likely that the solder joint failed. It's very seldom that a Predicta, or any other 57-58 year old TV will fire up and work on the first try, these sets are full of paper caps and old carbon comp resistors, which can stop both the vertical and horizontal oscillators dead in their tracks. This model is different from the other set in that it has a power transformer rather then being series string, I'm not sure whether these used the 2.4 volt picture tubes like the previous predicta models or not.
Regards
Arran