Hi BCGreg!
Sorry to hear of your trouble.
It may still be possible to recover your data using Target Disk Mode, as some others have been able to do soon after their drive has gone out, although some have not had success. Any of the Intel-based iMacs can be used as the Target, making the hard drive available to your mini or other iMac.
I have frequently used TDM with all three models of iMac G5 as well as with Intel Core Duo iMacs and never had a problem, but then I never had a dead hard drive to contend with, either:(
http://docs.info.apple.com/article.html?artnum=58583
I would try TDM first to try and pull off your data. If unable, then search this forum for Data Recovery. There have been plenty of successes with online software programs that can be purchased and downloaded to successfully recover data from a dead drive prior to pulling it and replacing it.
Later I would run the Apple Hardware Test to get an error code to give to AppleCare.
Best of luck:)