Clearer photo for you, guys
(image removed)
Take a look at the two "vertical canister" caps that are "between" the LED's and the right hand pot.
One of those two will be a 4.7uF cap (C1?), and the other will be a 2.2uF cap (C4?).
The 2.2uF cap ties to a 47 ohm resistor in the Rat, and I think I see it to the left of the canister caps in question.
That means the bottom of the canister caps in question should be 4.7uF (C1?).
To the LEFT of it should be a 56K resistor that SHOULD BE A 560 OHM resistor to be 1:1 with a Rat. Those tiny multi-band metal film resistors are hard to read, but 47 ohm will start out with yellow/purple/ ... / ... and 56K will start out with green/blue/ ... / ...
It looks like the culprit is the lowest of the three resistors to the LEFT of the two vertical canister caps. The two resistors in that part of the circuit are also tied together at one end, and I can see a trace clearly connecting them.
Or perhaps it would be easier to say that the culprit resistor is the lowest of the three TO THE RIGHT OF THE CHIP.
To be clear - THERE IS NO 56K RESISTOR IN A RAT. So by unsoldering one leg of the resistor in question and measuring it, you can VERIFY this with certainty.
Now - 560 ohm resistors are a little unusual at your local corner electronics store (e.g. Radio Shack). A 470 ohm resistor will be fine IMO. The bass will be slightly stronger, but not a deal breaker. Alternatively, you can put a 100 ohm resistor in SERIES with it, and orient them to make an upside down V at their junction.
Radio Shack should have the above sizes in both 1/4-watt and 1/8-watt. IMO, neither metal film nor carbon film is really critical, but get whatever they have in stock.
Also, a 680 ohm resistor can be used with negligible difference.
The resistor in question ties to one of two "high pass filters" (not to be confused with the Rat's filter control), and it's the LOW high pass filter - it allows bass to be mixed in at a lower gain level. With a 56K resistor, the filter will have a gain that might as well be zero. With 560 ohms, it's about 1/12th of the other filter with the 47 ohm/2.2uF combo. So whether it's 470 or 680 ohms isn't so critical - you get a little more or less bass at about the same ratio (1/10th to maybe 1/13th), and it isn't subsonic - it's around 60Hz. The ratio thing is just for illustrative purposes, and isn't really an accurate explanation, but should give a rough idea of what is going on...