I called a local appliance service person, who diagnosed the problem as a bad main power board and offered to fix it for a substantial sum. I found the part on Appliance Parts Pros and found it on my doorstep 2 days later (even though I only used the standard shipping option). Although Appliance Parts Pros did not have any instructions about how to install the part, I found a youtube video by ApplianceVideo.com that explained the procedure in sufficient detail. The entire repair start to finish took me 30 minutes and the fridge now works again.