As Jon says, take a look at something like
https://secure.logmein.com/products/free/ or
http://www.crossloop.com/ipage.htm?id=howitworks where, after a bit of setup, you could access the remote computer. The first is the free version of a product & doesn't let you transfer files, but you could probably just zip & email them to get round that (or use the 2nd option).