The brake light is on and I smell burning plastic

This happens pretty commonly with Hyundai cars... Try checking the fuse box.

Actually it's not "pretty common" with Hyundai or any other car :-) Sounds like a stuck brake shoe

since bot the brake and battery lights have come on you are losing charging voltage in the system somewhere. most likely the alternator. in my 11 years working on only hyundais(and unfortunately kia) i have never seen a melted fuse box not caused by an accident. i have however seen alot and i mean alot of alternator windingd melted.especially on the 99-01 sonata and the santa fe when it came out. the windings are coated in plastic and ust melt when the alternator stops charging. it is a very distinctive smell. have the charging system checked at a local auto parts store. that will tell you for sure