If you make the SSID and password of the new router, on the 2.4GHz band, exactly as it was before, then what Blink told you sounds correct. If they are different, have arrived with the default settings, from your service provider, I’m not sure how anything could connect back up?
I think you could find this quite tricky, and end up going through the whole set-up process again, if you can’t exactly match the SSID and password of your wireless network in the new router to that which your Blink system already believes it to be. If it is the same, you should be up and running, so I’m not sure what could be wrong then.
There is a way to change the wireless network only, but I’m not sure if that can be done in the absence of the previous network. Probably can, and I’m sure Blink support staff can talk you through it.
Good luck and let us know.