What size map are you playing? Try winning a huge map with 7 cities is a lot harder than on a normal map. If you go to the demographics screen, what is your land compared to the leader? I'm just curious because I'm currently playing a huge map/10civs right now and am finding it a lot harder than usual because the AI has so much land. I should have started the game with 18 civs so they couldn't expand so much.