Try for a Cultural or Diplomatic Victory
I took a look at that scenario and I have to agree that position is tough. bwarner and Andy Giesler have what I believe is the best all around advice. I suggest you take that no matter whether you take mine or not.
However, you're still likely to not be in a good situation. You won't have much production or land, and thus, not a strong military either. So I propose you don't play in a way that requires a strong military. Civ 4 has several win conditions:
Conquest/Domination (They're really the same)
The ones I've crossed out are the ones that require a lot of production or a strong military. Cultural and Diplomatic DON'T require much production of any kind. They do require commerce/science to research important techs which I believe you'll have, between rivers and cottages. (This can be supplemented with good trade relations, which you should have) They also only require 1-3 cities. (3 for cultural, exactly 1 with the United Nations built in it for Diplomatic.) If you can't expand to 3 cities, you should probably restart anyway.
Unfortunately, going for these won't work in every situation. The biggest thing that will stop your is your own play style. You must completely adapt to being nice to other nations and not building a military, aside from "police" units to keep your citizens happy. I always get an itch to go attack someone in the middle of the game, but I have a friend who repeatedly wins with these and NEVER attacks anyone.
Assuming you can adapt your play style, what empire/leader you are using will still have a big effect on whether you can even attempt these victories or not. Unsurprisingly, my friend's leader of choice for either of these victories is Hatshepsut of Egypt. [Creative, Spiritual] I imagine Ramesses II [Spiritual, Industrious] would have a good shot as well. (I mention Egypt because they happen to match where you started, and happen to be THE BEST at these victories. I'm sure other empires/leaders can work as well.)
Now, how to go about winning one of these ways:
Make friends with EVERYONE. Pay them tributes, give them tech, convert to their religion or spread your own, trade resources for the sake of trading resources (eventually gives diplomatic bonus, even if you get nothing out of it!). ANYTHING that will make them like you more. First, this means you won't need a military because no one will attack you, and, second, this is the way you win a diplomatic victory.
Found as many religions as you can, and build all the religious buildings. Remember to switch to Organized Religion so you make up for your poor production. Part of this is to get more culture, part is to manage who is what religion. One of the simplest things which makes people enemies is having different religions. If you found all of them, you (partially) control how they spread, so you can spread a single religion to every empire everyone will be friends (especially with you, who founded the religion). If you manage this, you get to wait until much later in the game to decide which way you actually want to win.
Finally, if you do try for these, you must commit to them early. Making nice with other nations and building culture add up from the start of the game. (Like just about everything else)
Edit: Consulted with my friend. (Who I hope to convince to answer questions himself, but till then...) He adds (with edits):
Technology choices also are pretty important...for diplomatic you need to found the UN, and for culture you want broadcast towers, so shooting for Mass Media is a good idea.
This reminds me: The most important structures to a cultural victory are the ones that increase culture by a percentage. Hermitage national wonder, Brodcast towers, and a special building for each religion (Cathedral for Christianity. I sadly can not remember the other names off the top of my head). Those require you to control more cities to be built, so more cities will certainly HELP, but are not strictly necessary.