If the cable is broken you wil need to replace it. What does it feel like when you pull on the release when in the car? If it is broken it is a question of where it broke. I don't have that year of civic so I'm not that familiar with how much space there is to get to the cable from underneath, perhaps someone else can check their vehicle. I did run into one where the owner thought it was broken but it was only the pull handle and we were able to open it using vice grips on the wire.

Good luck.