I have had a look at Roman Blacks website where this project is fully described and it looks as though the RC oscillator is not running, as you have suggested.
Why the oscillator is not running is a bit difficult to say.
Is the PIC you are using new, or has it been used before? Maybe the comparator has been damaged.
Another possibility is that the 16Mhz clock crystal is not running correctly.
If it was running very slowly, it would not measure the RC oscillator frequency correctly. However it is obviously doing something becuse you have text displayed on the LCD.
Apart form that, I have no ideas.
JimB