First thing to try is to sit right next to the router and then connect to it. What speed do you get then?
Second, is the wireless card in the computer capable of 108Mb? ie, is it an 802.11g card?
As for the other laptop not connecting, is it allowed access to the router? What are the router's security settings for MAC address restrictions? What are the DHCP settings? Maybe it can only dish out one IP address at a time, hence this 2nd laptop can't get one.