My Samsung TXJ2566 turns on and there is sound, but it takes about 60 minutes for the picture to come on.

Get a different TV as this one has given up the ghost.

Sounds Like The Flyback Transformer. That Would Be An Expensive Repair Job And The Decision To Fix It Would Depend Upon Age And Original Cost Of Unit. I Think This May Become A Fire Danger If Set Is Left On As Long You Say.