Test 3: Check the Link Lights
If you've made it past tests 1 and 2 (and the problem still persists), it's time for one of the quickest tests you can do. Look at your router or switch and make sure that the link lights for the device you are troubleshooting is (still) on. This may seem ridiculously simple, but kids are kids, cats are cats and bad things can happen to network cables even if you haven't touched them. The cat doesn't even have to chew completely through the cable either. Just piercing the outer shell and severing one of the eight wires inside is sufficient. Swapping the cable for a known, working one for a quick test can verify if that's the case or not.
Cables aren't the only culprit to problems at this step (but they are the most common). Power supplies on routers and switches fail from time to time. I've had switches that just decided not to switch anymore. If you run the ping test from step 2 while watching the router/switch, you should see at least one of the lights for the device blink to indicate activity. I had a switch that used to run just fine for about a month at a stretch and then just stop. All the lights would be on, but the link light never blinked indicating traffic being passed. In this case, just unplugging and plugging the switch back in may make it start working again. When this reaches maximum annoyance, replace the switch.
Occasionally one of the ports on a switch will fail while the others remain working. Try swapping the cable to an unused port (or temporarily try a used port, but don't forget to plug the other cable back in if it's in use). If the cable works fine on an alternate port, you might have been trying to use an uplink port or a port that has gone dead. In the latter case, replacing the switch is probably a good idea. I had an Ethernet cable that got hit by lightning during one particularly bad storm. The first switch, the Ethernet card on a printer, and another Ethernet adapter were killed instantly. However, one of the other switches was apparently among the walking wounded. At first one port stopped working, and then another. A good static electric shock can do this as well. I mention this to say that if you find one dead port on a switch, expect another and expect to be replacing the switch.