Don't take off the top grille, there is a danger with an old mic of ripping the whole diaphragm off of the magnet assembly.
To get inside the plastic sleeve, de solder the terminal bases with a solder sucker to free the wires that come up from below. Then undo the nut holding the paxolin board and with care the sleeve should slide off.
You will now see where the wires come from the voice coil and are soldered to another paxolin board. If you are lucky, one of them may have developed a dry joint over the years, and re soldering them may make it work again. But most likely, one of the very fine wires will have snapped off. This usually occurs when, over time, people have twisted the assembly around within the sleeve and the board works loose......