Battery Dead?

My wife drove her Acura to the mall yesterday morning to meet some friends. When it was time for everybody to get in her car it wouldn't start. The car battery has a history of losing charge (she drives only 6 miles to work, and some weeks the car sits a long time). They tried to jump start the engine, but were unsuccessful. Yesterday evening I tried the same thing with the same result.
Other symptoms I noticed:
- When the ignition key was turned nothing happened: no crank, not even any clicks
- Lights were all dead (headlights, turn signals, interior dome light, dashboard.) Whether the jumper cables were attached or not.
- 100% electrically dead except - the horn worked (same volume whether the cables were attached or not)
- I was getting amps thru the cables (big spark when I touched + and - clamps) but there were no sparks when I attached the cable to the Acura battery (+ to +, - to body screw, then - to - terminal)
I have no idea what to check next.