So, you have a stable WLAN signal (laptop 1 is on it). But lapotop 2 is not.
Test 1: conenct a UTP cable between router and laptop 2. Can you now
If so, the network in laptop 2 is up and running. If not you need to run a script to get it working. In Slackware I just edit /etc/rc.d/rc.inet1.conf and issue the command
but Ubuntu will no doubt do things 'better'.
My advice: use fixed IP's to get things running. If all works, you may go dhcpd.
When the UTP network runs, try to switch over to wicd.
When your computer seems to have a dead network, run as root and try again. If the problem is fixed now, it is a matter of privileges (it mostly is).