I have a 2000 Honda Civic. The latch that you lift to open the trunk suddenly stopped working. It is also?

In the latch area, there is the cable that has probably broken off and there is a solid metal rod that goes from the key lock to the latch and it has jambed because of it. Look up inside of the trunk lid after removing any covers to see if it can be reattached. Sometimes it is just the little plastic ends that need to be replaced.

It sounds like there actually may be something wrong with the latch rather than the cable. If the cable is broken then when you pull the trunk latch you should feel no resistance and it shouldn't return back to it's original position. If it does, then it's connected.

Since it even has a hard time opening when you use your key I'd say that it's the latch not responding properly. With the hood open, visually inspect the latch, turn the key and watch it's operation. You can also check the little hoop that the the trunk latches to for adverse wear and tear. At worst, you'll have to get a new latch.