Fortunately the tech support guy at Sprint knew that this issue exists and has warranty replaced the phone. I hope to have the new one on Tuesday.
Unfortunately, there is no known way to access the memory of the device without the touch screen working so I cannot retrieve my photos. I am going to call Palm support tomorrow to see if there is any way to access the device's memory without using the touchscreen to activate the USB storage mode.
Now what the hell do I do without my phone? I use it for damned near everything these days!
Update - There is a key combination that will put the phone into USB storage mode. I found it through Palm's tech support chat and it works perfectly. All my pictures, ringtones, books, etc, are now recovered.