If your power is no good then the PIC is not going to work. Try a 9V battery and a 7805 voltage regulator for power. 4.5V worth of C or D batteries may work also.
You could also try setting port a to all outputs TRISA = 0This should be done automatically by the HIGH command, but it's worth a shot.
The internal oscillator control register may also need to be set. I don't know what it defaults to, but try OSCCON = %01000100. Your editor will need to support the PIC you are using for this to work. Mine doesn't so I haven't been able to try it.
See if your teacher will let you use a different PIC. The 16F628 also has an internal oscillator and is much easier to use. The 16F84 is the old standby for hobbiests, but requires a crystal oscillator(no big deal, just a crystal and 2 22pF caps)