Right on Noodles.
A new build *might* help with ping.
There is a lot of debate about efficacy of
"gaming" network cards
, but the theory is that a better network card will give more consistent ping and the quality of the circuit paths results in faster ping as well. In the case of gaming NICs, a lot of the network stuff your processor usually handles is offloaded to a dedicated processor on the card. The point is that a superior network card, whether onboard or off, should help somewhat with ping.
Another element in ping count is extra stuff clogging up your bandwidth, such torrenting while you play, program updates while you play, anything that access the network. In the modern world that is just about everything on your computer
And yet another is firewalls and anti-virus programs. If you have a firewall running on the box, then you go through a router which acts as another firewall, and all your packets are being examined by your anti-virus, there are many opportunities for latency to be introduced.
I don't know about gaming routers.