Had a starting issue with the Civic today (2000 EX model - D16Y8)
The car hadn't been started in 36 hours, and went out to move it today, but the starter would only whine, no engagement. Sooo stopped the key turn, got out, popped the hood and checked everything.. seen nothing out of place, all grounds look ok and such... Got back in, turned again, same thing. I let off, and tried one more time, then the motor started to chug, and stumble for a few seconds, gassed it and it fired right over. I haven't been able to reproduce the issue. It starts fine every time now....
The engine had fuel and spark, it just wasn't turning over.. plus the engine wasn't rocking on its mounts.. but as it finally started to chug, the engine was actually moving some (guessing the starter finally engaged the flywheel)

so.. am i looking at a new starter soon? Going to replace battery as well, but was going to do that anyway before this issue..

 

This is also my first thought.

 

Pretty sure it is the original part so it's most likely due anyway...