Since you haven't posted any specifics about your system, I have to ask what the actual setup is. The attachments, although helpful, seem to show a different network.
Are you using a router. Can you ping it from both accounts.
The reason I am having problems understand, although I do not have any experience with using 2 users on a wireless network, is if your system was able to connect to the network, why is it showing such a difference in connectivity. In one snipit, you show a router (or something) in the next one, you are connected directly to the internet... I am confused.