Sounds like you're missing a fuse block somewhere given the amount of items not working.
Is the radio in the helm? If so, do you have an access door/panel you can open to see what else may be inside that compartment or at the very least be able to trace wiring??
Depending on the age of the radio you may have 2 or 3 power wires to trace. going off memory there's going to be a black wire (negative), red wire (positive - should go to a fuse), and there may be another wire, possibly red and smaller in gauge than the regular power wire, for radio memory.
**There will be other wires as well but these are the ones you're interested in to find where they're getting power.
Once you find that block, I bet you find where your dash switches are connected to.
***This assumes that all items are actually functional. Depending on age it is possible that your dash switches gave up the ghost as well as the radio. Unlikely all at the same time but if something was crossed when hooking up the battery something could have been inadvertently cooked.
