[Reece]

Comparing your pictures to the schematic, it would appear that it's all there. The coils wound with green wire are the RF transformers that are between the first three '26's and between the third '26 and the '27 detector. Also in the bottom view of the chassis, the two transformers at the lower part of the picture are the audio transformers that go between the '27 and the fourth '26 and between the fourth '26 and the '71. One of the pictures shows the power supply with its twelve terminals.

The radio is ca. 1927 per a note on the schematic but somebody kept it going into the thirties and perhaps later because the tubes are ST type rather than the globe type which would have been originals. The ST's came out in the early 1930's. This set would have used a high impedance magnetic speaker, I believe, but for testing purposes an output transformer and any PM speaker could be used.

The first order of business would be to clean everything carefully and then start checking with an ohmmeter. Typically the interstage audio transformers might be open. Not familiar with Kolster, but these transformers look similar to the ones on early Radiolas, and if they are indeed open, there are small replacement "guts" that can fit inside the original shells. You can also check the tubes with your ohmmeter: there should be continuity across the two fat pins which go to the filaments. Usually if the filaments are good the tube is good.

The power supply is going to be key to the whole thing; you want to pray that the power transformer is OK. Looking at the schematic, ohm all the windings out. See if any winding is shorted to the shell or to another winding. The divider resistor shows the ohms values on the schematic, should ohm those out. Some or all may be open, but they can be replaced with individual wire wound resistors. The 2 mfd. filter caps can be replaced with larger ones for better filtering as large caps were expensive back then. You could use 10mfd at 450 volt electrolytics. But as I suggested in my PM, follow up to find a Kolster expert on ARF. Then there are further tests if you get past all this.

This would be a fun one to fix up. Maybe not too hard to do!
Reece