I searched in vain to find a standalone part for the Rival 8401-M, but here are some leads:
You can call Rival and see if they still have the part in stock, although it is doubtful since they don't even have support for the machine on their website anymore.
I found several never-opened and used Rival 8401-M's in working condition on eBay and other places on the web, ranging in price from $16.00 - $35.00. For electronic products that are more than 4 years old, I reccomend buying used, because a unit that is NIB (New-In-Box) may be dead as a doornail (The analogy I use is this: if you have a Ferrari, no matter how well-built, and you let it sit unused for 7 years - when you go to start up that Ferrari after 7 years, it's not going to work because the parts have degraded, etc over that time period). Here is alink to an auction for a working, used Rival 8401-M
If your blade is broken, I did not find replacement blades anywhere on the web. If it is, in fact, the agitator that is broken, I have two leads:
Here is a web site that will show you what an agitator looks like (it is the tiny part that they are pointing to in red):
Ace Hardware, at one point, stocked the Rival 8401-M - if you take it in to them, you can see if they have an agitator that would work (if it is, in fact, the agitator, and not the blade that is broken).
My final reccomendation is tongue-in-cheek: Buy a new Cuisinart ice-cream maker instead - a simple one like the ICE-20 can be had for $20-$40 brand new.
-Tha Mp3 Doctor