FWIW: the "idiot light" has nothing to do with the battery. It is only a matter of "charge state"...
It ONLY measures charging voltage.
Check your megafuse if the light is always on.. located behind and below the coilpack.
Measure resistance across the two prongs.. should be nill to none. any resistance (if its busted, it will either read "INF (infinite) or in the MEGA ohms.. That is bad.
Ray