I am using external MCLR pulled high with a 4k7 resistor. That does sound like what is happening, except I am not using the internal MCLR. I am also using an external VDD, and I didn't terminate a VDD pin on my ICSP connector.

It is a surface mount chip, and I replaced it again.

I plan to order an 18F1220 as that has the enhanced CCP module, which my code is already written to work with. I was just trying to cut costs, but it has been a headache. I need a pin compatible chip to the 16F627A since I already have the PCB's, assuming I don't get this working.