Carrameow,

You can take the battery by Sears, Autozone or any chain store that sells batteries and they will load test it for free. Sears has a very good smart tester that is very reliable. You've nothing to lose but a little time. I've seen batteries go bad and do as you describe.

.0024 Amps is not enough to drain a good battery in anything less than weeks.

Best of luck,