to be honest phil, even with more details it is difficult to help since we can't see what is happening when you try to log in.
assuming you haven't already sorted it/given up, perhaps you can provide a bit more info by trying this link and telling us what happens
mail.google.com
when you go to this web site 3 different things can happen
1. If it detects you have recently used your PC to successfully log in to gmail it will automatically open gmail
2. If it detects you have used gmail before but have recently logged out it will redirect you to a page asking you to "sign in" (ie reenter your email address and password)
3. if it appears you have not used gmail before it will redirect you to a page that encourages you to create a new account
The web site does these checks by looking at the "cookies" on your PC - these are created when you visit websites like gmail and contain information about when you last visited and if you logged in or not. Cookies (generally!) make it easier to use services like gmail since they mean you do not have to log in every time you use it.
You mentioned you have recently deleted your cookies, in which case gmail will think you are a new user and will redirect you to the "Create a new account" web page
You should see an option to "sign in" in the top right - if not you should be able to get to it directly through this link:
gmail sign in
the sign in page should look like the image below.
Do you get to this point? if so, please try and login and tell us what happens next after you enter your email address and password.
I am sorry to say that if - after you log in - you are immediately returned to the "create a new account" page without any error messages then it will probably be hard to find out what is going wrong remotely, but let us know what happens and may be one of us can suggest a new test.