thanks for your comments.
pretty sure the starter is working fine. The whirring was a problem, but it apparently went away (have no clue why, but it did). Pretty sure the flywheel is enganging, at least it sounds like it.
No clue if I'm getting a good spark or not. If it makes a difference, the car runs great when it does start.
My guess is problems with the fuel system. Raul at Ultimate mentioned on the phone (based on what I told him) that it might be a problem with the pressure accumulator. Other posts on this website indicate that it might be a problem with the relay.
Could it be a problem with the fuel pump if the car runs fine once it starts?
We'll see, I guess.