These displays are multiplex: there are N anodes and M grids, so up to N*M segments can be selected. When some of the anodes won't light up, it means that those anode drivers aren't functioning properly, or the connections between the anode drivers and the VFD pins is bad.
You can test continuity between the anode leg of the VFD and the corresponding leg of the driver chip: if they are high or intermittent then the board traces or solder joints need repair.
If the continuity is fine, but the anode outputs of the driver chip never go high (high is from Vdd, +25 volts), those drivers are dead and you need a new driver chip. They are hard to source.