Photograph taken by L. Quagliotto, from Mazzeta et al 2004
First of all, I'd like to point everyone in the direction of Nima Sassani's Argentinosaurus entry detailing how he went through the steps of drawing his own Argentinosaurus. I could ask for permission to use his, but I would rather not wait and so will not put up any of his drawings today. Instead, we can start by simply looking at how enormous this dinosaur must have been. This vertebra cast, remember they did not find all of the vertebrae from head to tail, came from the thoracic region of the dinosaur most likely. The fact that the vertebra is almost as large as the average young lady, let us assume she is about 5'5" (165 cm), and that makes this part of the backbone extremely large. For this single bone to be contained in the back of an animal we can assume that the animal must also have been a gigantic animal and the size estimates, though taken from the legs and not the vertebrae that were found, attest to this idea of a gigantic dinosaur when all is said and done. So the question then becomes what would this dinosaur, whose skull and the majority of its body are missing, have looked like completely fleshed out?
The answer to that question may look a little bit like this. The long tail of Argentinosaurus was not as whip-like as the diplodocid cousins Argentinosaurus found in North America. The head, which has not been recovered from the earth at this point, is boxy, squared off, and short from nose to vertebral joining. That is a common setup for most large sauropods, and as such is nothing to get excited about; it is also probably quite accurate given what we know about sauropod's heads. The legs, of which a tibia and a partial femur have been recovered, are accurate in agreement with the majority of sauropods that have been found as well. The rear legs in this illustration are shown as more powerful than the front legs, though I seriously doubt and cannot think of a time when an Argentinosaurus would need those rear legs to rear up or those front legs to brace against a tree while rearing. The last thing that is notable about this illustration, and I am borrowing from Sassani's blog linked above, is that the chest is strong and barreled as opposed to a thin and weak chest. In order to support the estimated weight it would need to be strong, which makes the illustration more accurate.
Giants of Patagonia was a 2007 IMAX film that featured the work of Rodolfo Coria amongst his discovered and described dinosaurs, one of which, of course, was Argentinosaurus. The Argentinosaurus model used in the film was a little more apatosaurine than Argentinosaurus should be. The head is a little longer than we anticipate it to be, but the tail being held stiffly is a much larger problem in the model. The tail would have been held high for sure, but not stiffly out behind the body like a living truss bridge. The chest is also a little bit concave and weak looking, which, as discussed previously, is not as we anticipate we would find in an Argentinosaurus at all.