Netzero is an ISP, of sorts. I'm going to assume you're not using an email client like Outlook Express, but rather you're using a web-based service hosted by netzero, and you have some sort of netzero.com email address. e.g. "firstname.lastname@example.org".
Problems receiving email might be stuff being stopped by their spam filter. If you go to your webmail, there should be some sort of "spam" folder where all your blocked emails go. Open it up and see if there's something that should have come through. You can usually "teach" these systems to not block trusted senders by unblocking these messages. You might also be able to change your spam filter settings to be less restrictive.
Problems sending main are usually caused by the receiver's spam filter. Not much you can do about that other than ask them to unblock you in their spam filter.