Silock,
A lot depends on the settings for a game. When you say you usually have 7 or 8 cities, what is the map size? On a small map this is very good; on a huge map this is not nearly enough. Is there more land available for the taking, or has it all been claimed by other civs?
You sound like you have the basics down pretty well -- initial expansion, getting a tech lead, keeping your cash flow strong and your tech slider high, specializing your cities. So I am not sure just what is not working.
One possibility is that you should found (or capture) more cities -- my general rule is that if I am positive cash per turn with my tech slider at 70% or higher, I can afford more cities. Cities cost money, but they produce beakers and units and control territory and resources. More is usually better, as long as you can afford them. Since you say you are keeping your finances under control, this should be considered.
How strong are your cities? How large do you grow them, are they paying for themselves, do you have happiness or health issues with your citizens? What buildings do you build in them? Every city should be contributing something to your empire -- not right at first, perhaps, but certainly after it has had a few dozen turns to grow. You should know what it will contribute before you found it (or capture it).
On military, the AI is much stronger on defense than when Civ IV was first released -- many improvements have been made and conquest can be tough. If I am going to war, I usually have almost all my cities building military -- at least for a while, as I prepare my attack force. I will usually keep several cities turning out troops throughout any conflict -- your forces always gets drained, from losses in battle to garrisons for captured cities to units out for a while healing, etc. Units, units, and more units is the way to go -- military efforts are often about momentum, and having 50% more units can lead to much more than 50% faster conquest.
On diplomacy, there are a ton of factors which affect whether civs will vote for you. I find diplo victories rather frustrating, actually, as civs you have helped and gifted and worked with all game end up abstaining (or even voting against you) while other civs you never made a real effort with end up voting for you.
But if you do not have enough pop...that generally means you need more cities, and bigger cities. Take them from your enemies if you have to.
Anyway, just some thoughts from an Emperor-level gamer who used to struggle on Noble. I've learned a huge amount from these forums, and from reading (and later participating in) the game of the month and succession game of the month threads.
If you can provide some more details, or specific examples of things that caused problems, that would allow for more specific advice.