Battery on Honda Civic keeps draining

I have a 1994 Honda Civic EX-4 door with 300,000 miles. I bought a new battery 10/2007

and just recently another, but the car will not crank. It makes a noise like a whining cow. Then battery keeps draining. I do not drive it everyday anymore and I try to crank it and let if run for an hour once every 6 weeks. The last time it ran with no problem is after I gave the battery a jump, but now it just makes noise and eventually pops. However, it does not start. Again, I hear one loud pop sound after several attempts of trying to start the car. The car does not smoke or smell after hearing the sound.

I have a Honda service manual, but I do not know where to begin and which parts in the electrical system to test for. If I new what parts to look out for and how to isolate the system component, I probably could repair it myself. Are there any suggestions and reasons why this is happening?