The Good News is: 1.) These old radios consist of discrete components on circuit boards easily soldered and de-soldered. Are you capable with such tools and work? Replace ALL the capacitors if capable. Then power it up and listen. This is an internal power issue all right.
"Listened closely and I could barely hear a station while running at full volume. "
So, it still tunes, and passes audio, but fails to amplify.
The OTHER likely failure point, with the symptom described would be the 2 transistors, both of them on the outside of the unit, up front near the top. Those old bipolar junction units can burn out over time. If cap replacement doesn't do for you, replace the transistors. Equivalent FETs can be had now fairly cheap, if you fancy those over BJTs. More efficient.
2. An entire radio receiver and player board can easily be installed in that old chassis too. One can add bluetooth.
3. Folks occasionally sell working units. While not so common as Philco or Delco stuff, they're out there.
4. One can buy a modern unit, made for your dash. Pricey but best option if you have $$.