This is bound to happen eventually. One day you pull on the trusty hood cable release handle and instead of easy access to your dipstick, there is just a nasty "snap!" and a bleak sense of helplessness as the release handle flops around loosely.
These things bust in a couple of places. Sometimes at the handle itself, sometimes under the hood, either the cable itself or the fastening widgets that make it work. Either way you have to at least dismantle it, but replacing it is pretty cheap and quite easy (once you know how!)
My first experience with this was with a 1980 5000s which I would one day own. My boss was milling around his car with a co-worker or two, trying to pry open the hood, which had lost its cable that day. I jumped into the fray (I can never resist a good milling around), and once it was open I could see that a bit of baling wire and a T-handle in the center would make it work again. That T-handle was a piece of 10 GA solid core copper wire with a red jacket. Quite tacky, but it worked. When I later bought the car, I got silly and machined a nice little aluminum pull handle, threaded for an eye-bolt to yank on the baling wire. I still have that handle somewhere...
That is how you do the kludgey or temporary fix. Back when more European cars from the 80's were out there on the road, it was almost common to see them with random bits of hardware or wire hanging out through their grills - the owners ad hoc solution to broken release cables.
You do not need to do this! A new cable is cheap and easy to install! (am I getting repetitive yet?)
When my next car, a 1983 5000 turbo, lost its cable, luckily I called the local dealer to price a new one. It was only about $20, although this was back about 1987.
First you have to open the hood. If the cable broke right at the release handle, you might be able to get some pliers on it and pull firmly, opening the hood. Then you're temporary fix can just be a small vice-grip type plier left in place. I bought a used car that came that way.
If the cable or hardware under the hood broke, you'll have to locate and operate the release catches manually. The releases are on each side, typically slightly inboard of or behind the headlights. Each one has a spring lever which is pulled towards the center of the car by the cable. You can reach these levers with a screwdriver or piece of coat hanger, and trigger them manually. Each one has a loop about 1/2" round at the end that has to be pushed or pulled, letting the hood pin spring pop the hood up an inch or so. If you're having trouble finding them, it helps to be able to look at another car with the hood up. Try a bone yard, a friends car, or maybe a picture in a manual.
Once the hood is open, you probably will still need to order the parts, so one of the temporary fixes gives you underhood access until they arrive.
Installing the new parts is pretty simple. The old cable is easy to remove - you can cut it in a few places, but that isn't even necessary usually. Hang on to the hardware if you didn't buy any new stuff (you should...). There are two plastic bits that look like golf tees with holes through the center which put pressure on the release levers (the new ones are metal) and there is a cable stop clamp at the passenger side hood catch, at the end of the cable. There are also usually 3 or 4 plastic guides behind the sheet metal that the bare cable runs through. Either slide the new cable through the old jacket (lubricate it well) or pull out the old jacket and slide in the entire assembly. Attach it to the release handle end, making sure there are no kinks. Now thread it through one golf tee, the driver's side release lever, the little cable guides, the passenger side release lever, another golf tee, and slip on the cable stop. Gently remove all slack in the cable, pulling the golf tee things snug into the release lever loops, and tighten down the cable stop set screw.
Test it with the hood open - pull the release handle, and both release levers should be pulled towards the center of the car (it takes two people to do this... one to pull, one to watch). Once you have verified that the adjustment is correct, bend the cable where it exits the cable stop and cut off most of the excess. Then lubricate the cable, release levers, and hood latch with your favorite slippery stuff and go back to more important things, like driving!
Update: Brendan just went whole hog on his 1987 4000Q, and replaced the cable, all the hardware and even the spring arms which hold the hood pins closed - well, I did most of the fiddling with those, but anyway, they were actually pretty cheap and almost easy to put in. His hood now pops up with a simple single pull and click, like it should, like new. No more "click - clunk" as the two sides release separately. Nice.
We now know that the new "golf tees" are made of metal. Also, the new set screw part that terminates the cable is integral with the golf tee at its end - nice upgrades!
Here is a crude schematic diagram of all the major parts. It is not to scale, and the parts are "false colored" to make it easier to label them.
At SuffolkD's site you can see a lot of photos and animations showing how to open the hood when the release handle doesn't work on a type 44 (5000/100/200/V8) Audi.