What are some steps to troubleshoot problems sharing printers, files, and screen?
Please be more specific.  If nothing changed except for the router, though, let me ask: is the one machine plugged in directly to the network via Ethernet, and is the other accessing the network through WiFi?

If so, it may be that the router has a feature enabled called "WAP Isolation" -- basically it creates a separate network segment (or collision domain, if you like) for the wireless clients.  Try disabling wireless with the laptop and plug it in directly.  If it works, that's probably where the problem is.