Operating a PIC at 3V ?

[mister_e]

I would like to run my PIC16F876A at 3.0 or 3.3V. I would like to run the PIC at 4mhz. Will the PIC handle datarates of 9600 Baud on the UART pins?

Yes it will. Look the datasheet or use my SPBRG calc. with the right settings, you can have a 0.16% error wich is really not as this bad.

I have my PIC in the circuit and have an LEd tied to PORTC.0 to make sure the PIC is running. IT does not Illuminate the LED. What should I be looking for?

Once again, i'll bet on the Brown-out detect fuse. Disable it and post your results.