Some followup to what's been going on:
I got a Bosch remanufactured starter, put that in, with some small complications. First off, to do the starter from above, I needed to remove a ton of stuff out of the way to get access to everything:
1. Disconnect battery negative connection.
2. Remove airbox out of the car completely.
3. Realize that there is nowhere near enough space to work on the problem.
4. Remove the engine upper mount crossbar- the one between the shock towers.
5. Remove the Over The Engine pipe- this gives enough clearance on the passenger side to reach the hose clamp for the lower intercooler hose.
6. Remove the lower intercooler hose.
7. Remove the bracket that the airbox mounts to and is connected to the bolts on the starter.
8. Remove the electrical connections from the starter- the big positive cables and the smaller, spade mount.
9. Remove the bolts from the starter.
10. This was the tough one- my starter did not have a third hole, I have no idea what is the best way to break the starter loose. I used a pry bar and that was not a good idea.
11. Starter removed, replace with new one.
12. Reassembly is the reverse of disassembly.
The problem persists- the car does not start. With the battery fully charged and a new starter, it makes a loud whining, whirring sound when I engage the starter, but usually, it makes a kind of "hammering metal" sound when the starter turns over. I'm thinking I don't have spark or fuel for some reason. The starter sounds like it's trying to turn the engine over.
Any suggestions on what to do next? So I have a brand new starter in the car and it still doesn't want to start. I don't think there are any codes, no check engine light.