XR 500 can't detect internet but AC 1750 does just fine.

> [...] My old router is a Nighthawk AC 1750 and it still works. [...]

   "AC 1750" is a speed, not a model number.  Look for "Model" on the
product label.

   The non-psychics in your audience also can't see how it's configured.

> [...] comtrend vr 3030 modem [...]

   That looks to be a simple modem.  If your DSL connection uses PPPoE,
then you'd need to configure that on your (new) router.

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

> [...] The internet light is white/blinking white [...]

   What are _all_ the LEDs doing?

> [...] It must be my damned modem somehow not giving the XR 500 what
> it requires.

   Or, your (new) router is not giving your ISP what _it_ requires.  Or
something else is wrong.