[Arran]

If the speaker is shot the only source for a replacement electrodynamic speaker is one of the same design salvaged from another radio, usually another Philco but one from another set may work as well, it's best to confirm that the speaker has gone bad first . The field coil on the speaker should be connected between the electrolytic condensers in the power supply through a cable and a socket, the resistance should anywhere between about 500 and 1200 ohms on an ohm meter if it is good, if it isn't good you won't get any reading. One of the best ways to check if a transformer or the speaker filed coil is any good is both visually and with your nose, a burned out transformer will smell and look burned and may have blobs of melted tar around and below it. If it does not smell or look burned then it would be best to check the continuity of each winding with an ohm meter, I or someone else could explain this later and how much resistance each winding should have.
This looks and sounds like a big project even for an experienced restorer, if you haven't worked on anything like this before I would recommend that you find help or find someone else to overhaul it for you. Not only is their the possible damage caused by a short circuit but these early 40s Philcos were infamous for using rubber covered wire that deteriorates over time. There are three things that you must learn to overhaul an old radio, you need to learn how to solder, read and follow circuit diagrams, and use a volt ohm meter. It can all be learned with time but most people who start out in this hobby generally take on something more simple and in better shape for their first restoration project.
Best Regards
Arran