Hi hkyfn, I empathize with you since this is, of course, a behavior we would not expect from a brand new system.
This is very likely a problem with the antennas considering such poor signal strength when your system is very close to the router.
I suggest using a tool like inSSIDer 3* to monitor your signal strength. It will be good if you get between 0 to -30 dBm when near to the router but something over -70 dBm is not acceptable at 5 feet.
If indeed it is an antenna issue I recommend you contacting DELL* again.