Good morning everyone!
@Juanito yes, there was an error message at the startup about a missing radeon file, but per curaga's advice on loading the firmware-radeon file, that message has been resolved.
@curaga looking through the X log now that I've loaded the firmware file, I can see a whole bunch of RADEON lines so I'm assuming that X is working with the ATI driver instead of the vesa one. However, for lines that appear to be loading anything for audio, I see "No input driver specified, ignoring this device. This device may have been added with another device file." I can pastebin the logs if you desire. I also made sure I was loading the alsa-modules-3.16.6-tinycore64 file so I would assume this would bring in the latest alsa drivers.
I also wanted to perform the steps you mentioned using the 'Apps' software, but I don't see anywhere in there to update the dep files. I can only see an option for checking for updates and nothing about "Fetch Missing". I ended up updating all the files that were found, but now the system takes an extremely long time to get into X with only parts of the TC GUI loading (e.g. still has the default X11 X shaped cursor and no wbar). I'm just going to start all over with a fresh install...
Dave