I don't think you'll find anything wrong with the speakers, unless somebody has been deliberately poking at them. Try a known good pair of external speakers to isolate the problem. More likely the unit is in need of a fresh set of capacitors and/or a transistor or two. Also, as you say, it is soon 50 years old - you shouldn't expect that great a sound out of it, although it does sound nice when in good order.
The stereo light has nothing to do with the actual signal (except on FM). If you select the tape input for example, it should just light up. If it doesn't, the bulb has failed, its socket is oxidized, or the switch bank has bad contacts.
Spend a few minutes pushing every button on the switch bank if you haven't already. That often restores the operation (or you might hear where the problem is) and might even improve the sound in case there are oxidized contacts.