Sure, you just replace the XLR connectors with something better. You'll still have garbage cable but...
A multimeter (~$35) would come in handy, as they typically have a "continuity check" feature that will allow you to determine where the break in the signal is. If you tear the cable apart and you determine that the signal passes all the way through the cable, then you know that one of the connectors was to blame...otherwise the break is in the cable somewhere and you get to play "chop & hope".
I recommend Switchcraft connectors. They are an industry standard and can be found even at local electronic shops (not radiosmack). The part numbers for their XLR connectors are A3F (female) and A3M (male).
Slackmaster 2000