Unable to connect to Steam Servers

Hello everyone,
When I ask the server list in Steam, it just shows me (about 50 instead of 4000) and when I try to connect to one of them it does not work. The problem is not my firewall or my anti-virus, because when I disable it changes nothing.
The problem could come from my router. In fact I have a modem with a router Numericable which is integrated, but given that this integrated router running poorly, I have another Belkin, which works better.
When I open my control panel under "Internet and network connections", I learn that my IP address is 192.168.2.2 and the default gateway is 192.168.2.1. So I type 192.168.2.1 into the address bar of Internet, and transferring all the ports that I have been told to do to with Steamserver (on 192.168.2.2). All this is on my Belkin router. I can not do the same on the router to my modem because the requested IP address where you transfer ports is a 192.168.0. (X). However the problem lies perhaps with not the router.

Thank you for your help!

Would you mind trying a power cycle of the DSL modem and your router? I would like to see if after the line syncs back up if the issue still occurs.

you can try deleting the client registry blob file located here C:\Program Files\Steam...not sure it will help.
Close steam completely, delete Program Files\Steam\clientregistry.blob, restart steam. It will perform an update and then it should work. Always worked for me.

The only file you should delete is clientregistry.blob
If you have a problem still you should check the Steam forums on the steam site