It sounds like the network solutions serversdfo not like the resources needed to Send an email out to over 9000 recipients and keep trak of it. It may be that using a shared account for power messenger uses to many resources and you need to investigate a dedicated hosting plan, so as not to effect other users sharing your server.
With power messenger, the only form that is available to the general public is the registration form. and the registration form uses captcha to prevent bots from completing the registration.
Power Messenger also offers a setting to enable email verification, this would force registered users to verify their email address.
you could set the mailing audience to only send to verified addresses.