When getting a new router when using the Slingbox SOLO, you will need to reset the Slingbox and rerun the setup process. Below are links to reset the Slingbox, and where to set it up at:
If you are still having issues connecting remotely after doing this, you may need to setup a port forwarding rule for the Slingbox on your router. Below is a link that will explain what port forwarding is, then direct you to a how-to guide on how to do this:
Hope this helps!