Problems with sending and receiving mail on a second computer

Mail works OK on my first computer (iMac running OS 10.6.8) but I have endless problems with the second one -- a MacBook -- even though the settings are the same on both. Sometimes messages are received on the MacBook, but sending is impossible. WiFi settings are OK, and the MacBook is connected to the internet OK.

Another problem is that when out roving, I can't collect Emails at all when I am in wifi hotspots like cafes. I used to be able to connect to mail2web, but since the disappearance of MobileMe I can't access mail no matter what settings I use. Any thoughts please?