Thanks Geek-9pm,
I don't have any speculation intentions.
OK, let me detail a bit.
I have some ~10 devices in this network. Layout is this. Internet by optical cable comes to this modem/router, from there via Ethernet cable goes to my switch, from the switch again via Ethernet cables goes to some computers and to my WiFi access point, the rest of WiFi devices get internet from that access point. The access point DHCP is disabled.
When I monitor my network I do see assigned IPs like 192.168.1.2, 192.168.1.3, 192.168.1.15 ...
Before it was up to 192.168.1.19 I didn't pay a particular attention to. Only after that one laptop was assigned 192.168.1.20, the problem was detected. That's when I started manually setting above 20 to my other devices. And when I say ping goes through, this is what I mean. I was setting say 192.168.1.21 (anything above 19) to a desktop computer and pinging google.com or yahoo.com or anything, ping was going through, but anything else like Skype or browsing didn't work. When I was setting it to say 192.168.1.19 (anything below 20), ping asa well as anything else, browsing or Skype is OK.
Now, after they did their restart or reset of that modem, I don't know what exactly they did, I can set the IP to anything 192.168.1.21 or 192.168.1.101 or 192.168.1.218, everything is OK.
Regards