How to determine DC input voltage of a device without its charger?
There is really no direct way to know.  You can maybe guess by looking at current draw as a function of voltage, the battery arrangement, etc.

This is really not a electronics problem.  The obvious first approach is to ask the manufacturer.  2 years isn't that long.  Somebody should still know what the charger specs were.

Failing that, search around to find someone else with this device.  This could be someone trying to sell one, for example.  Maybe they will look at their charger and tell you it's voltage as a favor.