Okay, first of all thanks to all of you who showed interest in my problem and wanted/want to help me. I really appreciate it (This strong, smart and always helpful community here is one reason why I come here almost daily. It is a great place to learn things and it gives me the opportunity to lend a helping hand -though not as much as you all can- to those who have problems).
Grandpa, I went through all the suggestions and links posted (and yes, I'm running XP).
The default gateway IP is the same as my computer IP (though it is dynamic and changes every day). So, I tried this one in the browser address but ended up with FireFox not being able to load it. And just to make sure, I tried it as well with IE; same result.
But I accidentally typed a wrong IP at my first attempt and got to a page which was for log in and had already the username typed in as "admin" and also a password "****". So, I clicked on "login" without changing something, but the side just reloaded. Then I tried the both passwords suggested, but again, just a reloading of the page.
When trying to set up the static IP in my network connection, I'm ending up with a screen quite different to the one shown at "Portforwarding" (see screen shot "Internet Protocol TCP/IP). No Subnet Mask and no Default Gateways.
The only thing what I know now for sure is that I am firewalled (funny that I didn't realize this before, though I've seen it many times) -see gif "Network connection screen shot", although LW, FW and Phex do not recognize a firewall.
Any further suggestions at this point???