Can I use C3000 router when the input is not a coax cable but an ethernet cable?

> [...] If I swith to other ISP which feeds the router through an
> ethernet cable - do I need to switch the router?

   Yes.  Strictly speaking, it's bidirectional, so not an "input", but
Netgear Cxxxx models have no WAN/Internet Ethernet port, which is what
you'd need for use with a separate modem or ONT.

   Note that that does not automatically make your C3000 completely
useless in a different (non-cable-TV) environment.  If you have any use
for one, then it should be possible to configure a C3000 (or any other
Cxxxx model) as a wireless access point, but that's not a router.  For
details, 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.  But you'd still need a router with a WAN/Internet Ethernet
port.