Who is your hosting company?
double check that they support sending emails using the php mail() function from php scripts.
also double check the SMTP server and port number that they recommend using, in the power store admin section, on the store Settings tab, make sure to enter the proper SMTP Server address.
also double check the Store Email Tab and make sure to enter a valid email address for your domain for all of the various From Email settings.
On the gateway tab, what payment gateway is selected?
to operate in test mode, make sure not to select PayPal standard as the gateway.