I wrote my friendly Toyota customer service rep online and actually got an answer.

One of the questions was what happens when one runs out of gas. Does it damage the battery or anything else if I keep driving until it stops?
Below is the answer I received. Does anyone have access to additional information that would explain "Protection Mode" and how to reset it yourself?

From Toyota:
"We apologize; we do not encourage continuing to drive the 2004 Prius when it does not have gas. The vehicle will not be damaged by driving without gas, however, the vehicle may enter "Protection Mode." When this happens, it is possible that even after putting gas in, the vehicle may need to be reset by your local dealership to start.

We recommend gas be purchased when the tank reads 1/4 full."

 

I ran my Prius I out of gas once (the tank does not hold as much gas as they say). It ran about a mile, just so I could pull in at a gas station... It was a bit jumpy when I started it again, but I haven't noticed anything about it after this happened.

The way to reset it would be using a tool similar to Grahams miniscanner (don't think anyone has developed a miniscanner for the Prius II yet). I don't think you can reset anything with the Prius I miniscanner though.