Despite of resetting both ends of routers,they are still not functioning

As you probably know the PF code indicates Power Failure has occurred! To reset press the ON/OFF buttons, then make sure the time is set correctly! Should be good then!

You may need to reset your device and you will see a reset button at back of your router so all you need is to keep holding it for 10 seconds then unplug the power jack for like 1 min and then your device shall be reset.But please make sure to backup your all settings first.

Check if your LAN-cable is plugged into computer and in the other end of cable to wall-outlet/adsl-modem/some router /switch

If the cable is connected is the indicator light on both ends.

Thunder and lightning could have a electrical surge in the internet grid?

You can try a new AC adapter.If that does not work,it will need to be repaired by a Nintendo authorized center.(I used to work at one).If you do by a new one PLEASE buy Nintendo brand.The "off" brands usually end up in some kind of problem down the road.
Good luck and agme on!

Turn the monitor off.
Unplug it from the AC power.
Reconnect it, turn it on, and see if it returns to "normal".

Do you have house-insurance that covers electrical damage from lightning/thunder storms?

Your house may have Thunder rod installed on the roof. Your power network should be grounded, but it may be connected to thunder rod earthing, which is wrong. The earthing is not good. Check it.

If you haven't tried using the reset button, should be an explanation how to use it on the router in the manual, try that.
Also, try a replacement power supply to the router, if you can get hold of one. As this maybe faulty.
However, likely faulty router, maybe due to power surge, due to lightning/bad weather.

If you had an lightning storm you most likely have a bad logic board. That is not a reset button you are pressing.

There's ALWAYS the chance of damage.

If you have reset both the router and the cable modem and it still doesn't work, bypass the router and try connecting the system directly to the Cable/DSL modem. If your computer works in that situation the router has been affected, double check your connections between modem & router AND between router and computer.

If you still cannot connect, call your internet provider and inquire re: system status in your area. If all is good ask them if they can 'see' your modem. They will check their equipment to see if your modem is connected and communicating with their system. If they don't find it the modem is suspect.

If they can see the modem but you are still unable to connect to the internet via the router/switch, then the router/switch is the culprit.

Of course this all assumes everthing is OK with your computer. Otherwise this becomes a much larger troubleshooting issue. But let's not go there yet.

BIG TIP: Invest in a lightweight UPS or a line conditioner, particularly one that will protect your inbound Internet connection (coax or phone line) as well as the Ethernet port protection you need. In the end it's a LOT cheaper than replacing lightning damaged hardware.

Surge Protectors are of limited value because a majority (80% or more) of all power related electronic issues, especially regarding solid state circuitry, is due to BROWNOUTS, not surges. Something the manufacturers of surge suppression strips & related hardware are reluctant to admit, but that's why they can reliably afford to insure their surge protectors for ridiculous sums.

Apply this same principle to home entertainment systems, tv's (especially LCD & Plasma), game consoles, and any other valuable home electronics.

u can do one thing like changing the soft ware on the device and reboot it and check