Network Connection Issue: "The router cannot connect to the Internet with the current settings."

> I just switched to a WNR1000v3 hooked up to an SBG6580 router/modem
> whose WiFi seemed to be unreliable, [...]

   It's tough to believe that an antique like that could be the solution
to any ordinary wireless-network problem, but...

   "hooked up" how, exactly?  If the [ARRIS?] SBG6580 gateway is (still)
configured as a (modem+)router, then it would probably be wise to
configure the WNR1000v3 as a wireless access point, rather than as a
full-function router.

   Visit http://netgear.com/support , put in your model number, and look
for Documentation.  Get the User Manual (at least).  Read.

   When I did that, I didn't see a simple WAP option, but almost any
wireless router can be configured that way.  See, for example:

      https://community.netgear.com/t5/x/x/m-p/1463500

   That's written for a Netgear C6300-as-WAP, but the steps are about the
same for any other router (any make/model) which lacks a one-step WAP
option, including your antique.

   Note that that scheme leaves the WAN/Internet port on the
router-as-WAP unconnected.  (A WAP is all-LAN.  A model with the
one-step WAP option effectively reconfigures its WAN/Internet port as
another LAN port.  Without the one-step WAP option, you need to use only
the LAN ports.)

   General advice:

> [...] I can't ping urls via command prompt [...]

   "can't" is not a useful problem description.  It does not say what
you did.  It does not say what happened when you did it.  As usual,
showing actual actions (commands) with their actual results (error
messages, LED indicators, ...) can be more helpful than vague
descriptions or interpretations.  Especially when using a command-line
program, copy+paste is your friend.

> [...] seemed to be unreliable, [...]

   "seemed"?  "unreliable"?  See "not a useful problem description
[...]", above.