My car (99 Accord EX 2.3l m/t) has been having the same problem for awhile now. It started having problems starting and making a loud rattling sound. It now will not start without pop starting it. The starter just spins. I bought a new starter and same thing. I had both of them tested and they both work fine. I'm guessing flywheel but really don't know. I looked at it when I had the starter off and it looked ok through the little hole. Also if you think its the flywheel what's the easiest way to change it.

 

Strange....if the teeth are fine on the flywheel we are back to the starter bendix not "traveling" or contacting properly.

Changing the flywheel, call that a clutch job. bearing, pressure plate, disk, new flywheel, ect......

 

I just had a rattle the other day when i would let off the gas but that was due to my catalytic converter on my 98 accord lx. I jacked up the car and the rattle came from there.