The level of Dunqul Oasis and Dakhla Oasis is the last level of the Old Kingdom. Normally, after getting the victory screen for either mission, you'd get a screen with the periods (Kingdoms) displayed and the Middle Kingdom Highlighted, and if you select "Enter this period" you should see an introduction to the Middle Kingdom and then be able to choose between Thinis and Waset. If the game thinks that you haven't completed all of the levels in the Old Kingdom then it might not advance to the Middle Kingdom. Did you complete all of those levels?
One way to check the levels is to go to "Relive Family History" and select "Individual missions", which displays all of the missions that the game thinks you've completed. At least one of the missions from each level of the Old Kingdom (and previous periods) should be displayed. (This site's Walkthroughs page provides a convenient list of missions.)I think that the game stores the results for a given family in the file "family name".dat in the Save folder. (For example, on my system, there is a file C:\SIERRA\Pharaoh\Save\Brugle.dat for my family's results.) Make sure that that file does not have the property "Read-only". (You should also check the autosave* files in your family folder.)
Perhaps some other forumers will know other things to check. Problems with computer systems are best posted in the Technical Forum, but your problem appears to be in between that category and Game Play, so I don't know where you'd be most likely to get good help.