Windows – Remote Desktop cannot connect to the remote windows 8 computer from windows 7

"Allow Remote Assistance conenctions to this computer" isn't the option you're after, a little lower than that you should see a group of options labeled "Remote Desktop."

In that group should be three options, the default set to "Don't allow connections to this PC". Try changing it to "Allow connections from computers running any version of Remote Desktop (less secure)".

It'll also pay to go into "select users" and make sure the account you wish to remote in as is present and if not add it/them.

fyi remote assistance is more a tool for letting you help a remote user through a problem or showing them a solution, rather than opening a proper remote desktop session. http://support.microsoft.com/kb/300546 for more info.

If you have a NAT router, disabling the router firewall may not be enough. Did you set up a port forwarding rule?

To be able to connect to your laptop at home, you have to set up a port forwarding rule which forwards an external port of your choice to the internal port 3389 (remote desktop) of your laptop.

Let's say your external ip is 1.2.3.4 and the internal ip of your laptop is 192.168.0.20. You could then create the following forwarding rule:

1.2.3.4:55555 -> 192.168.0.20:3389

This would forward external port 55555 to the remote desktop port of your laptop.

If you correctly disabled the firewalls on your router and laptop, you should be able to get a remote desktop connection from work using 1.2.3.4:55555.