It's a Security Cam DVR and the ones I've seen were pretty old school!
One option is to change your router SSID and password on the new Vodafone router to that of your old router. The other option is to navigate to the WiFi settings page in the DVR and enable WPS, before pressing the WPS button on the router.
*WPS is a security risk, ideally you'd have this turned off and only temporarily turn it on when needed!
My fear is, that some of these units being quite old school, it's possible that the WiFi on the unit is only capable of WPA(1) authentication which may mean changing the authentication on the router to WPA/WPA2 authentication possibly even using with (horror of horrors) TKIP.
Unlike on TV streaming boxes you shouldn't need to perform a full reset, but poking around in the settings you may find some IP settings that need changing to the router subnet 192.168.1.x /24 (255.255.255.0), and the device may also benefit from being allocated a fixed local IP (outside of the routers normal DHCP allocation range but within the same subnet).
This all assumes that it's the DVR box that is the issue and not actually the App. If your mobile or computer that runs the app, can see the local network then it'll be the box and not the app!
