I was having the same problem with my 2004 Civic EX. After unscrewing everything apart and seeing nothing wrong with the wire on both ends (driver's and trunk side), I realized that my issue was with the hook on the fuel door that locks the door in place. It was simply too close to the spring, causing it to lock too "good." So I bent the hook away from the spring for about 1-2 millimeters and now the fuel door opens with no problem. Careful not to bend the hook too much or else it won't make contact with the spring, preventing the fuel door from closing. I hope that helps some of you folks. Take care.
You can also just use a long life sticky tape (I used Tuck Tape) to stick the cable casing to the floor so that it won't move when you press the lever. Also note that you should only press the lever half way down. If you press it all the way this is what will eventually break the plastic clip that holds the casing to the frame.
My fuel door opens fine but the trunk doesn't open when I pull up. When I use my key to open the trunk it works. Would you say the cable is snapped for the trunk?