I think this might be the post: Expired evaluation license of VMWare Workstation blocks free Player
I did an uninstall of the program, and then started rooting through the registry for any occurrence of vmware (Ctrl-F) and nuking it (not for the faint of heart).
I think what did it was finding the license key, which lives under a "VMWare, Inc." key (there are several of them) (Note that it wasn't under the path mentioned in the above thread).
I also cleaned out C:\ProgramData\VMWare, which contained cruft from various other VMware software products that I had been evaluating, but had uninstalled.
Thanks for the help,
Adam