I know this sounds crazy, but you could try pouring Coca-Cola on the battery terminals. It's possible the terminals and/or posts have oxidized or corroded from sitting, and this can compromise the connection, preventing cranking. The Coca-Cola will dissolve the oxidation.
In my taxi days, I was asked by dispatch to check out another driver's vehicle because it wouldn't start. Everything had power, but the starter would not engage. Poured some Coca-Cola on the battery terminals and it fired right up. The terminals didn't even look corroded or oxidized, but apparently that was the problem.