The php code looks ok for setting the cookies. The only part that I can see a potential problem with is the checkbox input you have in your form. You have it like this:
<input <?php if (!(strcmp(((isset($_COOKIE["remember"]))?$_COOKIE["remember"]:""),1))) {echo "checked=\"checked\"";} ?> name="rememberMe" id="rememberMe" type="checkbox" size="30" />
The problem is there is no value attribute, it is this value attribute that is being evaluated by the php code that is attempting to set the cookie. Please add in a value here, you can just set it to 1 and test the page. Let us know if this does not fix it up.