While mowing, my riding mower died. It's a Gravely G-series 16hp that
is 15 years old.

When the ignition key is turned from off to run, I hear one soft
click. The lights work in this state. If I turn the key from run to
start, I hear one loud click and nothing else.

The wiring diagram is shown he
http://home.attbi.com/~smschueler/Gr...iagram-big.jpg

The voltage (no load) across battery terminals measures 12 v.

When the key is in the start position, I measure these voltages:
8.0 v across brown wire from ignition switch to solenoid S10 terminal.
7.2 v from solenoid terminals S10 to S2 (terminals with small gauge
wires).
0.5 v from S2 to battery negative terminal.

As far as I can tell, the parts with safety switches are all in proper
position: Power Take-Off is dis-engaged, accelerator pedal is in
neutral, my butt is in the seat.

The connection from negative battery post to mower frame looks clean
and tight, and voltage from terminal to frame bolt is zero volts.

What do you think is wrong with the mower?

Thanks,
Teffy