The pieces were clearly very old, German-made circa the 1890s-1910. On a closer, surreptitious inspection, I discovered all the bits were there, and they weren't really broken, just unglued. Over the past century, the animal-based glue dried out and gave way.
It was the work of a couple of minutes for the pieces to be reassembled, and ta-da: here they are!
The 4 inch tall chair is made of red stained, gold gilt trimmed wood and pressed cardboard, while the faux wood grained sideboard is in a much smaller scale at 3 1/2 inches, and fits perfectly into my hard-to-furnish 10 inch tall dollhouse.
Not a bad find for a buck!