Cannot get channels programmed for RCA F27615

The chassis used in this set is one of several that are known for problems caused by bad solder connections. RCA used the metal shield around the tuner section to provide ground connections for several circuits. Cracks develop and all sorts of funny problems start to pop up. Tuning problems such as you describe are one of them. Often the troubles can be fixed by resoldering the required areas. Sometimes the bad connections can lead to failure of the memory chip that stores TV settings and data for the computer, but replacements are easy to find. A TV shop should be able to do the repair for you. RCA had several technical bulletins about this, although they never really admitted it was a design flaw, and there was a class-action lawsuit that resulted in a lot of repairs under an extended warranty.