The radio should turn on with the "VOL" thumbwheel. Should be a notch/click when rolling it all the way upward? With rolling downward being increased volume. Check the fuses and also that there is an operational speaker in place.
Check for a downloadable '67 or '68 Chrysler service manual at
www.mymopar.com
The battery will not charge or will not hold a charge after it's been on a charger? Trying to get the battery charged just by using the vehicle's alternator can take a long time and a lot of gas for it to happen.
If the battery (that came with the car?) might not desire to "charge", at first, put it on an automatic-controlled charger, at the minimum setting for an hour or so. If the battery's been discharged for a long while, it might take a while to get it to take a charge. Hopefully, with the little charge for an hour or so, it'll "decide" to take a charge and the automatic-regulated charger will take over. Make sure to do this where there is active air circulation! OUTSIDE. It might take a few attempted-charge periods for it to "come back", if it's going to.
Once the battery seems to have some propensity to take a charge, THEN the alternator can take over with the engine running, but it's best to start with fully-charged (or at least mostly-charged) battery for the alternator to work as it should. Providing the voltage regulator will let it. One of our members sells quality electronic voltage regulators, if you might need one. Making sure the battery terminals posts and the similar cable ends are clean is important! Or with the charger cables, to make sure they break through the surface oxidation on the terminal posts.
If the charger will charge the battery, but only to a certain point, no matter how long the charger stays on, then it's probably got a bad cell.
From my experiences,
CBODY67