Many thanks for all suggestions.
I have made several tests.

I deleted old wifi connections and made a new one (WPA2), however it did not help. I repeated it with WPA and even with Open wifi setting on router, again without any success.

With my laptop (Debian-Wheezy) connected through wifi (WPA2) to the router, I can connect to all of my email accounts without troubles using IMAP4.

At work, my n900 connected to Open wifi server or to Eduroam server works fine. At home, the troubles persist.