If pinging your local router doesn't work, there really aren't many possibilities:

1. You've made a config error and confused it. I'm pretty sure from that manual that its intended that you have (for example) 192.168.0.2/24 on the WiFi side and 192.168.1.1/24 on the Ethernet side—different networks. And the wireless side would be configured to route to 192.168.0.1 (your Wi-Fi AP). [Or, if your wireless network uses DHCP, you'd just set it to DHCP instead of static.]

2. You've made a config error on your computer, and you're running on the wrong IP address as far as the router is concerned. Try switching your computer to DHCP (ifdown eth0; ifconfig eth0 up; dhclient eth0 ought to be enough to test).

3. Its possible it has weird behavior if the WiFi link isn't up. Confirm that the link is up. (E.g., maybe it only brings up its Ethernet once the WiFi link is up.)

4. Your Ethernet cable is defective. Try a different one (yes, this can happen, and you can still get a link, and even unidirectional traffic flow)

5. Related to above, your Ethernet cable isn't fully seated. Can happen if the prong gets bent down. Gently bend the prong back out, make sure it clicks in securely.

6. You have a bad Ethernet port—physically or electrically, on either your computer or the router. Test with a different device (computer to a laptop and router to a laptop, for example)

7. the Linux Ethernet driver for your NIC doesn't work. Test by connecting your computer to a different device.

Original oneliner

ip link set arp off dev eth0 ; ip link set arp on dev eth0

Be sure to do it all at once, so you don't break network connectivity before you're able to turn ARP back on.

Interface discovering copy-paste command

interfaces=$(
  arp -n | awk '
    NR == 1 {next}
    {interfaces[$5]+=1}
    END {for (interface in interfaces){print(interface)}}
  '
);
for interface in $interfaces; do
  echo "Clearing ARP cache for $interface";
  sudo ip link set arp off dev $interface;
  sudo ip link set arp on  dev $interface;
done

Note: The semicolons allow you to condense this command into a oneliner, but it looks terrible in a code block on SO.

Example output on Raspbian

pi@raspberrypi:~ $ arp -n
Address                  HWtype  HWaddress           Flags Mask            Iface
10.0.0.1                 ether   58:19:f8:0d:57:aa   C                     wlan0
10.0.0.159               ether   88:e9:fe:84:82:c8   C                     wlan0

pi@raspberrypi:~ $ interfaces=$( arp -n | awk ' NR == 1 {next} {interfaces[$5]+=1} END {for (interface in interfaces){print(interface)}} '); for interface in $interfaces; do echo "Clearing ARP cache for $interface"; sudo ip link set arp off dev $interface; sudo ip link set arp on  dev $interface; done
Clearing ARP cache for wlan0

pi@raspberrypi:~ $ arp -n
Address                  HWtype  HWaddress           Flags Mask            Iface
10.0.0.159               ether   88:e9:fe:84:82:c8   C                     wlan0