Ok, I decided to tackle one sub-problem at a time, and just work on the phone. I'll try the suggestions you gave John, after I solve this one:
I tried connecting the phone wires directly to the phone, eliminating the answering machine altogether. Red to red, green to green. I also tried green and yellow together later.
[Linked Image from img14.imagevenue.com]

When I did this, everything works except for the ringer. I fiddled around a bit after recording the current setup:

[Linked Image from img255.imagevenue.com]
[Linked Image from img133.imagevenue.com]
Here is a better angle:
[Linked Image from img144.imagevenue.com]

I connected the line-in like this:
Yellow on "3" with the black ringer wire
Green still on "f"
Black still on "4"
Red on "L2"

And the ringer like this:
Black on "3" with yellow
Red moved to "L2" with line-in red.

Results: When I connect the phone line, the clacker moves hard against the bell that is adjustable (right side if looking at the bells), and stays there. Upon an incoming call, it rings weakly a few times and stops, and the ringing in the earpiece of the phone I am using stops too. It is as if I get one ring, and then nothing.

So, I put it all back.

I then found a schematic for this phone, and hooked up everything as shown again. The only enlightenment I got was the option of moving the green wire from "F" to "RR", so I tried that. I got nothing.

Question 1:
How many volts/amps is the ringer electromagnet so I can hook it up directly to something to see if that is the problem? I don't want to fry it.

Question 2:
Should I do that?

Question 3:
What am I missing here??