PIC16F723A Programming
It is NOT setup to power the target circuit from the ICD 3.


AN910 is a good reference on programming a PIC. It's worth a read, especially if you're having problems.

That being said, the most reliable way I know of to program PICs is to power down (i.e. disconnect the power source) and allow the programmer to provide power to the device.

There should be no problem powering your circuit from the ICD3. If there is (i.e. there's other load on the rail that the ICD3 cannot handle) then you may need some circuitry to isolate the rest of the VDD rail from the programming header (schottky diode or something similar) to facilitate programming.