What does the error code -4403F mean when doing the Internet recovery?

Those error codes generally mean your Wi-Fi is inadequate in some fashion.

Issues include:

Network-name (SSID) is hidden

Using a Manual IP address instead of good old DHCP

Using PPPoE configured in the Mac (configured in the Router is OK)

using certificate-based authentication

requiring a login screen entry

Using a Proxy

requiring the use of Virtual Network Connection to get any response

My mac not moving from that screen

Sfcrystalmethod,

do you have a HTTP proxy on your network? If you do, then OS X Internet Recovery won’t work with it while it’s enabled.