Insteon USB modem 2413U quit working when I installed Archer C7 AC1750 router

> I installed a Netgear Archer CD AC 1750 router last week. [...]

   That sounds to me like an "Archer C7 AC1750 Wireless Dual Band
Gigabit Router", which is a TP-LINK product, not a Netgear product.  But
an actual model number might help.

      https://static.tp-link.com/res/down/doc/Archer_C7_V1_UG.pdf

> [...] My Insteon home lighting network died instantly. The Insteon
> modem (2413U) [...]

   So far as I can tell, that's a device which is USB-connected to your
Windows system, and is not networked to any router, no matter who made
it.

   My quick guess would be that you did something unfortunate with the
power cables or the 2413U itself while you were fooling around.

      http://cache.insteon.com/documentation/2413Uqs-en.pdf

   It's not obvious to me that any Netgear device is involved in any
way with whatever your problem might be.