Do I need a new starter?
 

I have a 2003 Accord Coupe, 107K miles, new battery, and new alternator.

I am getting the "electronic buzzing" sound more often when I start my car. I realize that you need to turn the key fast, but this awful buzzing sound is getting more frequent during start ups?

Do I need to replace my starter?

If you have an aftermarket alarm it's possible the starter disable function is going bad.

Some early 7th gen Accords had issues with the ignition switch or starter cut relay which will result in the buzzing noise. You can try swapping one of the same type relays in the driver's under-dash fuse relay box to see if it makes a difference.

If you can start the car each time you turn the key the starter is working.

But what's with this needing to turn the key to start position fast?
Never heard that before. Is time delay related to the buzzing for your car?

Please update this when you find the problem. Thanks