I have a board with a PIC on it which I programmed so it is not protected.
The pic has no legible markings on it. Is it possible to read the PIC type?

 

If you have an ICSP port on the board, you can read a PIC that is on that board with the Pickit3 (with jumpers). This assumes the board was designed for this, as the data and clock lines should be isolated a bit (usually a small resistor) from the board's functions of those data lines. How did you program it in the first place? If you still have the programmer and can remove the chip from the board, you can read the chip as well with the same Pickit3 that you used to program it. You just need to follow the Pickit3 ICSP wiring examples.