i have a 1994 pnotiac sunbird that the handle broke off on the cable under the dash to open the hood. you can open the hood with a little patience and a fairly long screwdriver by releasing the latch under the hood. after this, on my sunbird, i just pulled the cable all the way out under the hood, tied it under the front of the car, and just pull it to release the switch. (thats only because i am too cheap and lazy to spend the money and time on a cable and install it.)
dodge truck broken hood latch
You can try unscrewing the grille and getting your hand or tools up to the latch.
The latch is broken, not the cable. You can still get to the cable where it is attached to the latch in the foot-well of the car. Grab the cable with a small vice-grip (or similar) and pull. Note that it is very unlikely the cable will break -the latch typically breaks before the cable since the latch is made from plastic and the cable from steel wire.
I had this problem on a Chevy; the cable was broken and had to be replaced. Before I replaced it, I was able to crawl under the car and, using a screwdriver against the cable (near the hood latch), pushing against the cable with the screwdriver, the latch released.
you can get to the latch through the grill
If it is just the inside handle broken off you can pull the cable with a pair of pliers. If it is in the middle, you should be able to reach up from underneath and cut the cable and then pull the inside cable. If the latch end has pulled off, you may be able to trip the latch from underneath, or take the grill out and unbolt the latch.
pull on the cable slowly with increasing pressure it should open or jack up the car and poke at it with a long screwdriver or pliers
Use a set of pliers to pull the cable even if the plastic latch is broken...
where your latch is broken at you can use a pair of pliers and pull the exposed cable wire and it should open best thing when u open it replace the cable wire
The cable between the latch and the handle may be broken or needs adjustement to shorten the cable so that the latch will fully release.
If the plastic part is broken, it can not be repaired. New latch is about $ 50.00.
The latch is under the front of the hood. The release handle is at the left side of the interior near the driver's door.