Is there any one setting in avast home that could be preventing a remote assistance connection from being made.
Both computers are running Windows XP Pro
I just ask you to take my word that avast is not involved in any way in preventing a remote connection assistance being made. I have gone through this so many times with the folks I support on avast.
Typically it is Microsoft system settings needed to allow remote assistance and, even more important if behind routers, the right services running on the systems and routers that support Universal Plug-n-Play.
Welcome to the forums, Dynamike. 
As Alan explained above, avast has nothing to do with preventing a remote assistance connection from being made. this is something controlled by the OS. Here is how to do this in XP:
http://support.microsoft.com/kb/306496
It is an easy find using … turn off XP remote assistance … as the search string in your favorite search engine.