2003 Honda Accord

Electrical problem
2003 Honda Accord 4 cyl Front Wheel Drive Automatic 68000 miles

I have been experiencing instances where my car will periodically crank slowly and then fail to turn over. On one instance with successive attempts the crank became progressively slower to the point where it would not crank at all. Headlights, interior lights, dashboard lights and radio still worked. Called for roadside assistance and a jump start was able to get the car to crank and turn over. I replaced the battery with a Sears DIEHARD GOLD but I am still having the issue. I had the alternator checked at a local auto-zone retailer. They claimed that it was fine. A friend suggests it may be a ground and at this point I am about ready to give in and have it checked out at a honda dealer.
December 3, 2009.

It could be the starter is going out, first I would check electrical connections at the battery, the negative battery cable to body, the engine ground cables, and the starter for looseness and corrosion.
Second I would inspect its drive gear and the flywheel or torque converter ring gear for damage.
If all those things are good, I would replace with a Honda Reman. Starter.

Thanks for your quick reply. The starter will crank at a normal rate many times however instances as mentioned in my first post are seemingly become more frequent. The same issue existed with my previous battery. I was hoping a new battery would resolve the matter. Alas that is not the case. The battery connections are solid and free of corrosion. Will a failing starter operate fine in some instances but crank slow and drain the battery in others? As I mentioned in my first post a jump start was able to get the car to turn after one such instance where the crank got progressively slower to a point where it would not crank at all. I purchased this car used about 2 months ago.

Dec 5, 2009.
Your car's component may have an excessive parasitic draw problem. That's why your battery is weak when you parked the car for a long period of time. It could be related to the B-CAN system.