Pinging an IP address is not affected by the DNS server used in your router. There is something more going on in what you describe. Ideally you want the following:
- Router is working and is the DHCP server and DNS server for the network initially. The router's own upstream DNS is something external, probably your ISP's DNS.
- You install Pi-hole and arrange for it to have a static IP (either manually or reserved by the router)
- Edit the router's DHCP setting so that it gives out the Pi-hole's IP instead of itself (the router) to clients to use as DNS
- Toggle a device off and on your network so it picks up the settings. Test that it's using Pi-hole for DNS.
If the router does not support editing the DHCP settings and changing the DNS, as CallMeCurious suggested, then you can switch to using Pi-hole as the DHCP server. That requires a little bit of planning, but first step is to confirm that you can make the change.