Teamviewer connection error: “Partner did not connect to router”, “WaitforConnectFailed”

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.

This sound like an administrative problem the fact that VNC protocol seems the to be working (teamviewer and ammyy are VNC clients) fine. Which would indicate that it is either a User are RDP setting on the server. If your company use's an Active Directory get them to check the session limit under the sessions tab(If it's windows of course), also if this is happening to more that one user it, get the administrator to check the RDP Session Host Configuration for the override setting.