I have an 03 Accord man. trans. 4 cyl. I replaced the battery 3 months ago and a week ago replaced the starter. When i leave the car off for a while it starts up normally, however, if I turn the car off and run a quick errand i try to start it and it will not turn over. It makes a buzzing noise! I am not sure if the time the car is off makes a real difference or not, it could be coincidence. The guy who replaced the starter told me he had the same problem and that all he did was keep the clutch in turn the key back to the off position then on then off and it started again. He informed me that there was a problem in the "ignition" (i.e, a bad connection with the key or something) and that it will work for a while, but eventually will stop working all together and that I should take the card directly to Honda for this problem. I dont know much about cars, but the ignition switch was replaced a few years ago. Once or twice I kept holding the key to the start position and after 5 or 6 secs the car finally started. This is frustrating and have put way more $ into this car than it is worth over the last 3 years. Please help I do not want to have to take it 30 mins to the closes HOnda dealership and spend another $350 +

 

Check the battery connections to be sure they are clean and tight.

Just me but this sounds like an issue with the battery, battery connections or the starter....yes, I saw that the battery and starter are fairly new but based upon your description that is what it reads like. When the starter is hot, it takes a bit more "juice" to get it to spin.