1985 Nissan 200sx battery was replaced and now the car won't engage to start?

First, why was the battery replaced? If there was a pre-existing problem (like a bad starter, for example), replacing the battery will not solve the problem. If, however, the car started fine before battery replacement, then the problem could be that the battery terminals (clamps) were not sufficiently tightened. Don't laugh, but there have been instances where the plastic cap(s) covering the new battery's positive and negative terminals were not removed (duh!). Remove those plastic caps.