That 1 Ohm resistor supplies DC to the audio stage. You probably have a faulty op-amp (U402) which is drawing excess current, hence the resistor gets hot and essentially fuses. Could also be a short in either C405, C406, C407, C408.
All of these parts are readily available. You should be able to quickly verify the issue with an Ohm meter, then remove the parts I mentioned starting with U402 until you see something greater than about 1k Ohm from either of the op-amp supply pins (4 and 11) to ground. You'll also need to replace that resistor again.
Edit: I should have read the entire post - yeah, if it's been worked on then there's a good chance there's a solder short to ground on either C407 or C408, check that first.
