I've had similar problems with by 2003 EX. Last year it would refuse to crank on occasion, but after a couple of whacks around the battery it would crank. I wound up replacing the positive cable, which in the parts diagram I believed is called a "sub-wire assembly," or something similar. It's pretty easy to replace if you take off the exhaust manifold and throttle body. It began happening again two months ago, but with reduced cranking speed. I replaced the starter with a $75 Rock Auto replacement, and it's been fine ever since.