Chameleons need to be stimulated to drink in captivity by simulating rainfall, the stimuli in nature. Just having a drip system available does not guarantee a chameleon will drink from it, and most often a chameleon will not seek out water from a localized drip unless it is very thirsty.
Most chameleons respond to being sprayed gently, but heavily with very warm water (it will cool a bit as it passes through the air) that falls on them like rain until they relax, close their eyes and begin lapping motions. At that point the drip system can be positioned so that it drips onto the chameleon's head and runs into the mouth. The chameleon will usually drink deeply for around a minute, but sometimes longer. The flow rate from the drip system should be rapid, approximately 30-40 drops per minute, and the water warm. This procedure must be performed daily. If this method does not work, then the caretaker must find another method that stimulates a drinking response so that the chameleon is OBSERVED drinking a significant amount of water at least every 2 to 3 days. If this does not occur it is likely that kidney failure will be the eventual cause of death. This is the unfortunate fate of more than half of all captive chameleons.
Some of the symptoms associated with kidney failure are anorexia (not eating), lethargy, sunken or closed eyes, and a weak grip, all of which your chameleon is now displaying. If this chameleon has not been ingesting a sufficient quantity of water as described above, then it is likely that this is the primary disease. Kidney failure is always fatal, but the chameleon suffers as the disease progresses from the gradual build-up of uric acid in it's blood that can form painful needle-like deposits in the joints. The chameleon may suffer for several weeks before it finally expires from the combined effects of kidney failure, starvation, and dehydration. A veterinarian can humanely euthanize your chameleon to end it's suffering, and all vets should know how to perform this procedure. If the vet you see needs a consultation, have him or her contact the Association of Reptilian and Amphibian veterinarians at www.arav.org.