How to find out which end of a dead battery is the anode, and its voltage
I see the two wires are red and black.  Very likely the red is positive and the black negative.  This is a very common convention, but of course, there is no guarantee that any one pack is wired according to the convention.

One way to check this is to use a bench supply set to 9 V and a low current limit, like 100 mA.  See if the device operates with + applied where the red wire went and - to where the black wire went.

You say this device is old, so these are probably NiMH or possibly even NiCd batteries.  Either way, figure about 1.2 V per cell during most of their operating life.  With 8 cells, that comes out to 9.6 V.  9 V should be safe to apply to the device but still allow it to operate.

The 100 mA current limit will likely be exceeded if you try to run any of the motors.  However, the point of the test is to see if the electronics power up and react properly.  If that works, and the current limit is hit when you try to command any of the motors to run, then you can try increasing the current limit.  It might take as much as a few amps with motors running.

Putting any remnants of the old batteries in your mouth is a bad idea.