[Mondial]

Before you do anything else, you need to check the wiring and see how the AC line cord is connected. If it connects to a power transformer, then the set can now only be powered on AC.

Also, see if the tube filaments are wired in series or parallel. If it is configured as a DC set, then filaments would be in series. If they are in parallel and connect to the power transformer then it is only AC.

The other question is how is the 81 rectifier tube connected. Does the plate connect to a power transformer or directly to the AC line. What does the ballast tube connect to? You need to trace out the relevant wiring and draw up a rough schematic before you proceed any further.

In any case, using a 1N4004 diode would not be relevant. It is sometimes used in AC/DC sets with series strings of 0.3 Amp filament tubes, which is definitely not the case here.