16f872-1
Hi !
If you do not know what component is not working (the PIC or the crystal), you have some options:
1) Try a new 16F872, burn the same hex and replace the old PIC (check and verify the hex codes programmed). If it works, your old PIC is bad. If it does not work, the problem should be in your oscillator section (xtal + capacitors).
2) If you don´t have another 16F872, try to use an external clock (a function generator for example or even a simple 555 astable oscillator). If the circuit works, the problem can be your crystal+load capacitors or the gate (inverter) inside the PIC. If it does not work, you are unluck, the PIC is damaged.
3) Replace crystal and capacitors. When soldering, due the overheat, capacitors and crystals can be damaged.
I had an experience with a 4MHz crystal. It oscillates for a while and after some period of time it stops working.
Unfortunatelly, the 16F872 has not an internal oscillator, so you are dependent of external or xtal oscillators.