Hopefully your cable is not broken. (It sounds like you have some tension, so
this is good.) Your front hood release mechanism may just be full of grit,
causing more resistance than usual to popping the hood open.

My 1991 Civic's cable became overstretched after a couple of years. The hood
release lever no longer worked. I removed the end of the cable from the hood
release lever and for years used pliers to pop the hood open.

Last year all the grit that had gotten into the front hood release mechanism
made it more difficult to pop open. (I had never cleaned the front hood
mechanism.) I didn't have the strength to pull the cable so the hood would open.
So I rigged up the car wheel jack in the foot compartment so that it grasped the
end of the cable. I was able to jack the cable far enough to pop the hood. Took
about half an hour of maneuvering to get the jack set up so as to pull in the
proper direction. I may have used a block of wood or two to position the jack
correctly.

The hood release mechanism is held in place by maybe half a dozen screws and
clips. I removed a grille (three screws) above the bumper to make access easier.
I thoroughly cleaned the front hood release mechanism using WD-40.

After drying everything, I applied a small amount of white lithium grease to
moving parts. This made a huge difference. I was able to pop the hood using the
pliers as I had been doing for years.

Coincidentally, a related post came up the other day. Yesterday I put a
half-hitch in the front release end of the cable, shortening the cable, and
re-attached the other end of the cable to the hood release lever. Works great
now.

I think all hinges, hood, and trunk latches are supposed to be cleaned and white
lithium grease lubed about every two years.

Updates welcome, particularly if you end up having to go in from the bottom of
the car. I'm not sure this is an easy do-it-yourself job. Groups.google may have
more on this.

"George Elkins" <netnews.20.elkins@spamgourmet.com> wrote
> I no longer can open the hood on a 95 Civic EX sedan.
>
> The cable seems to have no tension and pulling on the hood release latch
> inside the car has no effect. Battery is dead too. Short of towing to
> Honda dealer, any ideas?