try connecting the battery to the input any way (polarity is not
important as the input is ac)
the battery power will run through one side of the (probable) bridge
rectifier inside. so long as the stereo will run at that level and has
no specific requirement for AC all should be fine - you won't kill it
whatever happens.
......................................................................................
A comment. A little off topic but might raise a question?
Was in a RS many years ago where an employee was openly 'butchering'
the power supply section of an AC mains operated audio amplifier
wiring in a small 12 volt battery charger/power supply of the type
then used for 'desk' operation of mobile 12 volt CB sets.
I politely asked what he was trying to do and if I could look at the
circuit schematic on the counter! He said he was trying to get the
amplifier to run on 12 volts in his car!
Whereupon I noted that the 60 hertz AC to DC power supply in the
amplifier had +12 volt and -12 volt outputs!
His single 12 volt power supply (only 3 amps maximum) wasn't suitable
and possibly too small anyway! Often wonder what happened to that
piece of equipment!