2003 Honda Accord Periodic slow crank can has partial start

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.