Current Transformer with pic16f877a
Your circuit doesn't make much sense.  The two resistors attenuate whatever signal is produced by the CT by a factor of 2 and shift it up 2.5 V.  Is this really what you intended?

What current range do you want to measure, and therefore what is the expected output voltage of the CT?  Without knowing that, it's impossible to say whether it's doing what it's supposed to or not.  Start by just putting the load resistor on the CT and measuring the voltage.  Do you get what is expected?  If so, work forwards thru the circuit to see where you are not getting the expected signal.  If the signal seems right at the PIC pin, then any remaining problems are in the firmware.

I'd expect you would want to amplify the CT signal before it drives the PIC pin, but you also have to make sure a current spike can't cause a voltage outside the PIC Vss to Vdd range.

A TL082 is inappropriate here.  Look at its overhead voltage.  It's not going to do anything useful with a 5 V supply.

The power is connected backwards to the opamp, or you labeled the pins backwards.  Either way something is wrong since you have the more positive power at the bottom of the opamp symbol.

You realize a CT can only measure AC current, right?  You won't get any response out other then a short blip if you put DC current thru the hole, regardless of how much current.