The first thing to do is check for a thermal fuse in the transformer primary, it will almost certainly have one and is likely responsible for the open circuit. With care these can often be replaced, though they usually need to be crimped rather than soldered for obvious reasons. These chargers used to run pretty warm even when working perfectly, so any lack of ventilation or charging packs with shorted cells could cause overheating.
It's a charger for 7.2v NiCad packs used in cordless tools, with an output current rated at 0.8A. If (as is likely) the charging the circuit is some kind of linear regulator this gets you at least some way to the required transformer specs.
A 7.2v pack has 6 cells, and each a NiCd cell can peak at around 1.55v during charging. This gives a maximum pack voltage of 9.3v, so the rectified output of the transformer must be at least this high, plus whatever the drop out of the charging circuit is under maximum load. More inspection of the charging circuit will be needed to nail down the requirements, e.g. is the rectified output smoothed (these old chargers often used very low value reservoir caps so lots of ripple). How is the current limiting circuit designed e.g. a simple power resistor or a constant current circuit? These old chargers tend to be fairly simple, so reverse engineering the relevant parts of the schematic shouldn't be difficult.