I'm reading all this back and fourth here and it seems we are missing a couple of key setup questions.
1. Is this Apex hardwired or wireless to your network?
If it is wireless to your network, have you configured that wireless bridge with the new WiFi network, if not, then start there.
2. Do you have DCHP enabled on your Apex? DHCP is what most devices have enabled by default, but it seems alot of people used static IP addresses with their Apex. This is likely a carry over before Fusion existed and you needed to do port forwarding for your Apex. DHCP is kind of like a device asking the network for all the details to connect to the network. If its disabled, then your device must be manually configured and you have to know what your doing. So, make sure DHCP is enabled. To do this, go to your Apex display screen: Go to System> Netsetup> DCHP> then restart the Apex from the Netsetup menu.
3. Don't worry about the firmware update. IMHO, that will always be an engineer's first suggestion. But since your Apex was working before the router change on whatever version of firmware would allow you to connect to Apex Fusion. So updating the firmware, while its always a good idea, isn't going to get you connected to Apex Fusion.
4. If you continue to have trouble, then contact Neptune Systems support. They stay busy, but they will make time for you after the weekend and have you up and running in no time.