Why do living fossils like crocodiles remain so constant and not evolve?
Evolution is a process of change by four mechanisms; mutation, migration, drift, and selection.

You are correct in thinking that, because crocodiles have been around for a long time, they could have accumulated many new mutations in that time, relative to other more recent species. However, mutation is only one of the important mechanisms underlying evolution.

How different are ancestral and modern crocodiles?

It seems the appearance of crocodiles has been fairly unchanged since their occurrence ~85 million years ago (mya). 

How can they remain so unchanged?

Genetic variation may have been low in the ancestral population, this would reduce the potential for evolutionary change, as most change would have to occur through new mutations. It seems the populations of ancestral crocodiles were quite small, such that a genetic bottleneck may have occurred (which would reduce genetic variation). Mutation rates seem to be relatively low in crocodiles (also see here) which would reduce the rate at which novel mutation occurs, reducing the potential for evolution.

Note that many mutations will be neutral in their effect (or "synonymous") so won't have an obvious phenotypic effect, so there may be substantial evolution at the genetic level despite the phenotypic similarity. 

Low rates of evolutionary change could suggests some other things may have also played a factor. Given that the populations have been through multiple genetic bottlenecks, genetic drift could have slowed down rates of evolution eroding genetic variance, removing rare mutations from the population. 

If selection has been fairly constant over time then there is less chance that changes will occur. If selection were to change and favour new adaptations then these are likely to spread, but if selection remains fairly constant over time then it will continue to favour the same mutations. After a long time of consistent selection it is likely that most mutations will be deleterious (have a negative effect) and be removed from the population by selection. Darwin suggested that living fossils could occur because the environment they are in has remained fairly constant (from this link).