re. 'rail splitter': I didn't realize that your circuit (as you've followed Tangent's instructions) has a passive virtual ground - consisting of R1+/- and C1+/-. A rail splitter is a voltage regulator IC device that generates an exact midpoint voltage between its 2 inputs. It's an improvement over the basic CMoy design that you've implemented. See
http://tangentsoft.net/audio/cmoy-tutorial/tweaks.html#vground. Sorry about that red herring!
OK... I'll share my experiences when things were not as they should be during my CMoy construction. Firstly, I found that the amplifier section of the curcuit is pretty robust. Indeed my opamps have taken quite a bit of abuse (only one supply connected, output shorted to supply rails, etc) and are still working fine. Any problems were usually traced to the power supply. So, I think that you should start by validating your circuit's supply.
The following steps may overlap some of GermanGuy's advice, but I am focusing on the power supply. Before you follow any of these steps, convince yourself that the action(s) make sense to you.
1. Remove the opamp from its socket.
2. Calculate the theoretical current draw on your battery:
a. I'm assuming 9V at the battery; measure your battery's actual voltage when disconnected from the circuit.
b: LED current: (9-2)V / 10,000 Ohms = 0.70 mA (2V is a typical forward voltage drop across a red or green LED; you can measure this in your circuit across the LED terminals when it is illuminated)
c: Virtual ground bias current: 9V / (2 * 4,700 Ohms) = 0.96 mA
d: So, the current should be no more than 0.70 + 0.96 = 1.66 mA (actually less, depending on the battery's internal resistance). Anything in addition to that would likely be leakage through the filter capacitors (C1+/-). There is no other route for current to flow, right?
3. Measure the current draw from the battery when connected to the circuit (let us know if you need help with this). If it's more than your calculation, then you've likely got a problem with the electrolyte filter caps. They don't necessarily show visible damage if they're blown, but they often short-circuit internally, resulting in exaggerated leakage current. That's what happened to me (my caps) when i got the polarity wrong.
4. Measure the total supply voltage (voltage between battery's terminals with battery connected to the circuit) Measure the supply voltages referenced to virtual ground; these partial voltages should measure exactly half of the total supply voltage (+/- 2% assuming you've used 1% resistors as specified in Tangent's parts list). Again, if there is an imbalance, you've likely got a problem with one of your filter caps. The cap with the highest leakage current would be the one with the lowest partial voltage reading.
5. Verify that the voltages at the opamp socket's V+ and V- pin positions are the same as at their respective battery terminals.
5. If the measurements in (3), (4) and (5) were as expected, you have validated your power supply. If the measurements in either (3) or (4) were not as expected, then remove the filter caps from the circuit and repeat the measurements. If the readings are still incorrect, I'm afraid your problem lies elsewhere. In any case replace the removed caps with new ones; don't reuse any that you've desoldered from your pcb.
Let us know how this turns out.
cheers, Ewald