Cannot ping XP by ip or name.
If you still cannot ping the XP machine minimally by IP address this would suggest that some filtering is being done by some hardware or software present on you network or on the XP machine itself.
So once more back into the properties of your network adapter, select the advanced tab and then the settings button and then the advanced tab,
You should see, near the middle of the resultant dialog box a frame titled ICMP, click the settings button there and make sure that there is a check in the box that says allow incoming echo request packets.
OK your way back out of there and reboot.
If still no joy, then you need to consider what type of software products have been installed on the XP machine. I know you said that you are only using MSE (and I can pretty much promise that MSE is not responsible for this at all) but we have often chased these types of issues only to find that a member had, take your pick (AVG, Norton/Symantec, McAfee, Comodo, ZoneAlarm, etc.) previously installed on the computer and had uninstalled it or them by using the control panel applet but had failed to use the vendor specific proprietary uninstaller and consequently there were still remnants of the product left behind resulting in similar if not exactly the same problems as you are experiencing.
So if in the past (XP is almost 10 years old) you have had one or more of these products installed you might want to consider googling for their removal tool just to see if there are parts and pieces left that may be causing these headaches.