How do I dispose of an old Jump Start portable battery when it no longer takes a charge?

I had a set up that plugs into the house AC outlet to charge, has a set of cables attached to clip onto a car’s battery leads, and will charge up and start a car with a dead battery. But 7 years has taken its toll. It won’t take a charge any more.

We tried to turn it in for recycling at the Western Auto outlet where my son bought a new battery for the car we wanted to start, but they only accept car batteries. Still, the portable has lead and acid in it, so I don’t know if it’s OK to just throw it out with the trash.

I’d really like to find some company capable of properly recycling it and using the good lead that’s in it. Any ideas?