radio has been not saving stations like the battery had died. lights on dash dim

Blown fuse and misfiring cylinder. Have fuses checked and engine scan tested.

Check fuses to see if the radio has lost is keep alive memory power. The check engine light flashing indicates the computer is sensing a mis-fire, that's the roughness that you feel in the engine. That's going to need to be diagnosed. Start by pulling codes and identify which cylinder(s) are mis-firing.