From personal experience, I'd replaced ALOT of these working at the dealership. It wasn't just the accords either, it was quite a few Honda and Acuras that used the same design and power delivery system.
The most common issues I saw out of probably close to 100+ failures of these was:
- Ground strap on the starter becoming corroded.
- Bad ground to engine
- Your power lead corroded
- Bad ground or relay for your ignition.
- Bendix pin or the solenoid on the starter itself not moving smoothly.
I will say that more times than not, it was the starter itself. Usually the pin would get corroded and jammed, or corrosion would occur on the connections at the starter itself. The fact that it starts up probably means that "Something" is wrong with the starter itself. Couldn't hurt to clean up everything while you're doing it though =)
Also that sound could very well be the starter, but it is a bit reminiscent of a relay or circuit breaker going bad. When the coil inside the relay burns, or the armature gets contaminated by something they can sometimes act up and look fine but will make that odd whining sound. Just food for thought though, I'd replace the starter and check all your cable while you're there.