You might take a look at thumb wheel switches.
Each of the 1k LEDs would have to be individually wired to a 4 switch 'and' group, but it would be fairly straight forward.
The selection procedure would be strictly manual, and would not reset, but would remain at the last input.
The 7000 series military/industrial version looks promising:
**broken link removed**
.... maybe contact the manufacturer for additional information.
... On second thought ..... this method is going to be a lot of effort to wire up correctly.
However, there ought to be some way to do it without using a PIC or other microprocessor. ....