When I went back to the Pro that was wireless enabled but also now accessing IE / the Internet.
I notice here that when you connect the XP by wireless successfully there is
no Internet Gateway Network Connection, whereas earlier when the wireless failed there was an Internet Gateway.
That is caused by having a setting in the router of uPnP ON. I had a similar problem with XP whereby wireless would not always connect until I switched uPnP OFF.
I believe by turning uPnP OFF in your router will solve your problem and all this confusion and messing about with IPs is a red herring.
Just to check that you have not confused your IPs, what are the listed Connected Devices in the router and what are the IP & DNS settings of :
Network Connections (in that screenshot) / R click individually both the Wireless Network Connection & the Local Area Connection / Properties / Internet Protocol (TCP/IP) Properties ?
1999: Freeserve 48K Dial-Up => 2005: Wanadoo 1 Meg BB => 2007: Orange 2 Meg BB => 2008: Orange 8 Meg LLU => 2010: Orange 16 Meg LLU => 2011: Orange 20 Meg WBC