My speedometer was not working at all when I bought the car.
There are several videos out there to help you fix this in different ways, and they really helped me.
The DeLorean speedometer works by a cable attached to an angle drive attached to the inside of the front left wheel, and as the angle drive rotates with the wheel, it basically goes via a wire straight to the speedometer in the instrument cluster. This is not technically completely true, the cable from the angle drive is actually divided in two, where the one from the wheel and angle drive goes to the Lambda Counter in the footwell under the steering column, which turns on the Lambda Light in the dashboard every 30 000 miles. That is all the light is, and indicator that the car has run 30 000 miles, and you may want to consider a service. The light can be reset by a button on the actual Lambda Counter.
There can be a few things causing the speedo not to work, and the easiest way to find out is to start at the wheel. You need to jack up the car and remove the front left wheel to get to the angle drive.
Once the wheel is off, there should be a plastic cap in the center of the outside of the hub, which holds a short piece of spring/wire that goes through the hub and into the the angle drive. If this cap is missing, and it often is, that is your first point of failure. Then the wire to the angle drive will not spin.
The second thing is if the short wire/spring through the hub is missing or damaged. It should stick out a few cm out of the hub to attach to the plastic cap. On my car, both the cap was missing, and the short wire/spring was cut off and stuck inside the hub.
If everything else is working (the angle drive, the speedo cable, the actual speedometer etc) you can replace just the cap and/or the short wire/spring, then spin the hub or grab the wire with a power drill and spin it in reverse (the same direction as the wheel would spin) to see if the speedometer moves, but in my case it was not possible to get the cut off wire/spring out without removing the angle drive.
The angle drive is attached directly to the 32 mm nut on the inside of the wheel hub and attached to it is the speedometer wire, coming out from the footwell on the drivers side. You can start by loosing the speedo wire from the angle drive by unscrewing the metal cap at the end of the wire. Then what you are looking at, is the actual angle drive.
It is basically just pushed into the 32 mm nut and locked in place with a small retainer ring that fits in a grove inside the 32 mm nut. So you need to get the nut off, in order to get to the retainer ring, to then get the angle drive off the nut. But as you will see below, even though I finally managed to get the 32 mm nut and the angle drive off, I could not get the retainer ring out, so I ended up cutting the angle drive. More on that later.
To loosen that 32 mm nut you need to use an open spanner, since the angle drive is in the way of getting a ring spanner on there. You will have the easiest fit from the front, pushing the wrench up and turning it clockwise, looking from the outside of the hub, but you will apply more force if you attach it from the rear and push down on it. However, to fit the wrench from the rear though, you need to loosen the two nuts holding the disc brake caliper to the hub. The caliber can still be attached to the brake line, but don’t let it hang on the line, try to rest it on something.
As described above, the 32 mm nut has a regular thread, meaning it looses to the left and tightens to the right, when looking at the nut from inside the wheel. From the outside, you thus need to loose the nut by turning it clockwise. I had to apply a lot of force to the spanner to get it loose. First I tried banging the wrench with a heavy hammer (mind the front fender!), I tried using a jack to push it from below and just putting all my wight on it to make it come loose, but to no avail. I sprayed it with WD40, not sure if it helped anything, but at least it didn’t hurt. Still, the nut was stuck stuck stuck. I also tried loosening the outer hub nut, which on an -83 DeLorean is a 36 mm nut, on earlier car it is smaller. This nut is easier, because you can put a socket on it and use a breaker bar. I read somewhere that loosing this nut should make the inner nut come off easy, but it didn’t. I still could not get the inner 32 mm nut loose. What finally solved it for me, was cutting the wrench in half in order to fit a square pipe over it and use for leverage. The pipe was about 150 cm long and with that force the nut came off pretty easy.
But as mentioned above, once I had the nut with the angle drive off, I could still not get to the retainer ring on the bottom. There is a special tool you can get, but I didn’t have it. So I ended up sawing the angle drive in two pieces with a hack saw, since I was replacing it anyway, to be able to get the new one in place. Once you had sawn it off, it was pretty easy to knock the remaining part of the angle drive, still in the nut, through the other side.
Then you can reattach the new angle drive in the nut (don’t forget the retainer ring! With delorean go.com you get the ring with the angle drive. Otherwise you need to purchase it separately, or reuse the the original one if you can get it out.) Screw the 32 mm nut back on, really tight, reattach the speedometer wire to the angle drive, screw the outer hub nut back on tight if you loosened it, then put the short wire/spring through the hub (mine came separate so I could fit it from the outside, sometimes I think it is attached to the angle drive and needs to be pushed through the hub from the inside) and push the plastic cap back on the hub so that it fits over the spring/wire that is now sticking out of the hub. Grease all parts lightly with a high friction grease. You should not have to grease the inside of the angle drive it it is sealed, but the original ones has a grease nipple. At this point with everything attached,you should be able to spin the angle drive by turning the wheel, or use a power drill and spin it on reverse. You need help from someone to see if the speedometer moves. If it does, you are all set!
I managed to get my speedo working this way, but if this does not help, you may need to replace the actual speedometer wire. You can either use two parts of the wire like the original, where the lower attaches to the lambda counter, and the upper goes from the lambda counter to the binnacle. Or you can skip the lambda counter completely and use a long wire directly from the angle drive to the binnacle. There are good instructions on how to loosen the binnacle to access the speedo online: