There are a number of reasons why this might be. The most obvious would be host resolution. Often when trying to connect from one host to another, the user specifies a hostname (either local or canonical) that is human readable (ex. "host1.mydomain.net") which is translated into an IP address at the machine level. When they communicate, they identify themselves to each other almost exclusively via IP address.
If the XP/wired host cannot resolve the XP/wireless host's IP address for some reason, then nothing would happen. Can you ping with the IP address in one or both directions?
Let's assume that you thought of this and XP/wired actually can't ping the IP address of XP/wireless (but the converse works). This would be a very odd problem that shouldn't happen unless something like a firewall is interfering.
You have said that you have turned off firewalls but that is where I would look. In particular, I would anticipate that the XP/wireless' firewall is the problem.
I have assumed a number of things that you didn't specify up to this point. Please review the steps I have laid out and get back to me with details if nothing has improved.
This was first published in November 2004