The answer is yes
I assume that you want to transfer data ( which are files)
With the router you have both created a connection for the two computers and an home network to share files
How to do it:
1) easiest way and to show you it can be done
download this :
http://www.networkmagic.com/
It will work for file sharing for 30 days. After that it is still a most useful functional program
2) My suspicion is that you want to move files from one computer to another over the router
Here is the easiest way
get two separate messenger accounts
- yahoo , msn , skype whatever you like
http://www.oldversion.com/program.php?n=msnm
http://www.microsoft.com
http://www.microsoft.com/products/info/default.aspx?View=22
http://www.skype.com
log on on each computer with one service
i.e log on your two yahoo accounts
Then just send the file from computer one ( use one) to computer two ( user 2)
The messenger service will easily connect the two computers / accounts
the files will be sent not over the internet but over your router at very high speed
Lastly once you know what you are doing you can set up a hamachi private network
https://secure.logmein.com/products/hamachi/
http://en.wikipedia.org/wiki/Hamachi
Summary - the easiest way is log on each computer with a separate yahoo messenger account and send the files to other computer
you may want to compress files with winrar or wnzip to make for less amount to transfers of files rather than doing them one by one
http://download-winrar.org/
http://www.winzip.com/index.htm