I spoke with my friend Thom at work who encouraged me to try self repair. He pointed me to repairclinic.com which had an excellent diagram showing exactly how to remove the front panel and the location of the water pump. It also had a suggestion in the user forums to lay the drainage hose flat and see if any water came out -- which would indicate that the hose was unclogged and that the pump was to blame.
We did this, water came out fine, and so I removed the pump. Aimee had already called a couple of places in town and found replacement pumps for around $80. As I removed the pump, I noticed something clogged inside the pump's rotors. After removing it and reintalling the pump, everything started working perfectly again!
So thanks to the web, we saved ourselves probably $200 in doing the self repair. What's interesting to me from a web perspective is just how useless Frigidaire's support for their product was and that free community-driven web sites were able to provide so much more value. How hard would it have been for Frigidaire to have schematics and repair instructions and suggestions up on their web site for owners who were willing to try? They just don't get it.