Hey Linker_Split, it's all the same dialog. Loading anything, or saving when the application doesn't know the name of what you're saving (a new tournament, for example), or checking auto-save (because it has to ask for the filename the first time), all of these things display the file dialog, and that's what's broken somehow.
I still don't know what the root cause of this issue is, and I still can't replicate it myself. Rolling back IE has been the most successful method of fixing the issue. See the instructions in my last reply (just before your message) for rolling back IE. And cross your fingers. If rolling back to IE9 fixes the issue, and you're feeling brave, you could then upgrade again to IE10. Since I can't replicate this I can't say if it will work for you or not, but some have reported doing this and the file dialog still working.
I also had someone very recently report that rolling IE back to the previous version did NOT fix the issue, but afterwards they disabled all Internet Explorer plug-ins and that DID fix the issue. Your mileage may vary.