I had a bass like this where the G string was like that.
it's the bass. sadly enough I don't think there is any solution what so ever. I went though everything and tried really hard to like my old bass with the nearly silent G string, and ended up selling it and taking the biggest loss I think i ever have on an instrument sale.
weirdly enough, i clearly disclosed the issue in my ebay ad, and the new owner claimed he didn't hear it at all - i think he was a guitarist who had no ears... so, there's probably someone who can love this instrument how it is.
Good luck sorting this out!
Was it a stingray par chance?