driver side floor light plugs into the fuse box, it may be blown or just need a good wiggle to clean its contacts, the radio need power all the time to keep its memory and has a separate power wire just to do that, especially if it is not the original radio.
Change the BAT fuse and see if that helps, they can sometimes look good and not be and then sometime it can be as simple as pulling the fuse and putting it back in will fix the problem.
just as a note of interest, I would rather pound my balls flat with a sledge hammer than hunt down an electrical problem !
And I don't know why someone mentioned the lighter because I didn't see that in your original post, but then my memory is shot,
Technology is great when it works,
and one big pain in the ass when it doesn't
Detroit iron rules all the rest are just toys.