So, Proxmox runs on your laptop, and it boots with no problem?
After booting, does it show a login prompt with just above that the address where the web interface can be found? Is that the address you'd expect?
new to proxmox and virtualisation
But not new to Linux and networking? Proxmox is plain Debian with some magic glue to make virtualization easily accessible and manageable.
After you log in, you can follow networking troubleshoots for Debian.
You already tried pinging your router, but did not tell what the reply was. Does the laptop have a static IP or is it configured via DHCP? Things to search for, for starters, are `/etc/network/interfaces` , `ip address`, `ip route`. To check the boot log, try `dmesg|less`, with space bar for next page, q to exit, / to search.
Good luck!