The WN511B is a 2.4GHz card; the WNHDE111 is a 5GHz bridge/repeater. Those 2 will never talk to each other.
The Satellite would need a card like
http://www.linksysbycisco.com/US/en/products/WPC600N instead... or an internal card - I didn't look to see what Toshiba offers specifically for it - there are many vendors that offer internal a/b/g/n cards, but most notebooks don't come with a 5GHz antenna, so plugin cards usually work best for that.
According to the Gateway website -
http://support.gateway.com/s/Mobile/2007/Godzilla/2906040R/2906040Rcl4.shtml - the P6312 doesn't come with a wireless card, though the user manual clearly shows the switch to turn it (and the bluetooth module) on and off on the corner under the user's right hand. The Realtek driver offered for download also works for 3 different Realtek variants of the same chipset - models WN630xL (x=0 integrated, x=1 PCI-e and x=2 Mini-PCI), but those are 2.4GHz-only, also... so it doesn't make sense that the SSID of the WNHDE111 shows up in that at all, unless it has an optional wireless card in it that's not mentioned on the Gateway site.
Do you know what wireless card the P6312 has in it?