Oh, dear, I'm not sure I can help. Your pc/internet link should not naturally be set to allow remote access.
Well yes and no !
The Yes part: Most people who have a broadband connection are hidden behind a NAT firewall.
To explain that a little better, your local network addresses have no correlation with the address you appear on the internet as thus any in bound connection attempt needs direction to the local address it is for and if it cannot figure this out/is not present it is denied.
NAT (Network address translation) is the method whereby an outgoing request is paired with the appropriate in bound request - for example if local address 192.168.1.1 is talking on port 3384 to google the router knows inbound requests on 3384 from google are for the machine on 192.168.1.1 and forwards it accordingly.
The application you were using for remote assistance is not part of windows (remote desktop was not introduced until XP) this is publishing its presence somewhere and allowing the remote user to pick up the link and connect thus bypassing a NAT firewall (basic principles on how gotomypc etc work).
Make sure whatever it was you installed is disabled or you risk the integrity of your machine.
As an aside - most routers will allow port forwarding, this is whereby you can specify a port e.g. port 80 (http) to be forwarded to a particular machine on the network - this is how you would set up a home web server to be visible on the web even tho its behind a firewall.
The No Part:
If you are directly connected to the net, e.g. via a cable modem (note: not cable router) or an analogue modem/ISDN terminal you will need to install your own protection/firewall as you will be directly visible to the net on your machine - thus any inbound requests made to your publicly exposed IP address will be forwarded direct to your PC for dealing with and if no software firewall is in place may leave you open to abuse.