I afraid, the cookies are dependent on the browser's and to use cookies for session management, it should be enabled in the browser being used.
And for your information, asp pages use cookie for session management and it run perfectly. Thus the reason might be your code, i.e, please verify your php script to set cookies. Even try other browser, like Mozilla Firefox, Opera, Netscape, or what you would like.
One thing I would like to admit is that the cookie are of two types persistent cookies and in-persistent cookies. Only the former is stored in the cookie history of the browser, while latter die with browser, when closed. To set persistent cookie, you need to define certain properties like its expiray date.
I think this might give you some insight in your problem. 8)
