@dennisr40 

Hi,

Check if your WR841N has the setting "Forbid Ping Packet From WAN Port". If it has that option, then you need to disable it.

Furthermore, is the "public WAN IP Address" you mentioned the same WAN IP Address as shown on the status page of the WR841N?

In case it isn't, then make sure your have setup port forwarding correctly on the device that your WR841N's WAN port is connected to. 

  @woozle the WAN IP Address is not shown in TP-Link Admin.

there are some websites that show IP address.

  @dennisr40 

If your TL-WR841N doesn't show the public IP address, then I see two possible scenarios.

1) Your Internet Service Provider is routing your Internet connection through another NAT router on their side (CG-NAT).

   -> In that case you will not be able to access that web server behind your TL-WR841N from the Internet.

2) There is a modem router at your home that introduces a NAT.

   -> In that case you might be able to make it work by either setting up port forwarding on that modem router or switching that modem router into a so-called "bridge" mode.

What is the "Connection Type" of your TL-WR841N's WAN connection? Is it set to "PPPoE" or "Dynamic IP" or something else?

  @woozle The router is connected to a Speedport W925V.

because it has no VDSL modem.

I think I have to buy this router: TD-W9960v

  @dennisr40 

Well, what you are going to do is up to you.

According to the user manual of the Speedport W925V it allows the user to configure port forwarding ("Port-Umleitungen und Port-Weiterleitungen") and it can also be switched into a pure modem ("Speedport als DSL-Modem nutzen").

In which Operation Mode are you running the TL-WR841N? Is it "Wireless Router", "Access Point" or "Range Extender"?