You are remembering your calving days with some accuracy. :)
There are a number of different possible disease syndrome that immediately come to mind based on your description of her presentation. The treatments for each vary significantly so, as I'm sure you'll understand having worked for vets, it is difficult to say exactly what treatment is required without a accurate diagnosis. It is also tricky to make a diagnosis over this format, without being able to examine the animal.
The short answer is that the cow needs the local vet soon (or 3 days ago), but I know you have your hands tied there. I will try to cover the most likely and common problems that might be affecting this cow. I hope it will at least help you convince your neighbour of the urgency of the situation.
The first condition is retained foetal membranes (RFM), which is when the placenta does not pass, or pass completely. When his occurs, the uterus is at great risk of becoming infected as the membranes become putrid and allow bacteria to grow inside her. In most cases, the membranes are passed in the first 8-12hrs. So anything longer than that is considered to be RFM. The inflammation and infection of the uterus that results from RFM is called metritis. Antibiotics and anti-inflammatory medications are usually required. In severe cases, the uterine infection spreads to other parts of the body once it enters the bloodstream. This is sepsis, or septicaemia (bacteria in the blood).
The second possibility is that the breach birthing has resulted in some injury to the cow herself. Sometimes, when the calf is either large, or presented in an unusual direction, it (particularly its legs) can damage the birth canal. In the worse cases, the calf can kick through the wall of the uterus and/or the rectus, creating a hole that communicates with the rest of the abdomen. This type of injury requires surgical intervention, pain relief, and usually antibiotics.
If the cow is unable to rise, and is showing any unusually neurological signs such as twitching, tremoring or weird behaviour, there may be a metabolic imbalance in play. The most common two problems that occur at this time (around calving) are low blood calcium (hypocalcemia), and low blood magnesium (hypomagnesemia). Both of these result in weakness, since they are required for nerves and muscles to function properly. Be careful if you see signs of aggression. This can be seen with low magnesium, and can make the cow very dangerous. Treatment is through IV administration of calcium and/or magnesium to replenish what is critically low (through a drip together with IV fluids). It may be possible to obtain calcium (as calcium gluconate) for subcutaneous injection in feed stores, but it is usually not effective due to poor absorption.
Glucose may also be low if she has endured a long, tiring birthing, or has not been willing/able to eat since. Treatment may therefore also include IV glucose in the drip. If you can get her to keep eating, this will likely help with restoring blood glucose levels.
Lastly, it would be ideal to have a vet perform a rectal exam to rule out the possibility that there is another calf that she has not been able to pass. If there is a second calf, it will be dead by now, but it still needs to come out. This would cause illness in a similar way to RFM (but with some 40-50kg more "material" inside to cause a problem as it putrifies inside). Unfortunately, there is no way to know if it is there without an exam.
I sincerely ***** ***** neighbour gets his cow seen to sooner rather than later. If he ends up deciding not to have her seen for whatever reason, it might be worthwhile discussing with him the possibility of putting her down to end her suffering. You might be able to find a vet or local animal welfare officer, that can come out and put her to sleep for relatively little cost (possibly no cost). Or some farmers would do this themselves with a shotgun, which is not unkind if done properly.