How to check with a simple multimeter whether an old lead-acid battery and its charger are still working?
With the battery connected to the charger, and charging up, I would expect to see something like 7V (give or take a fraction of a volt).  Once the charger is disconnected, the battery would drop to about 6.5V when freshly charged.

If the battery is only giving 4.5V, then it is totally flat.  If it has been left like that for years, it is unlikely to ever work again.