I have just recieved a Telstra Gateway Frontier but I am unable to connect my HP 3630 to it. When I am using the printer software to connect, it is unable to find the printer. I had it previously connected to my old Gateway Max modem with no problems.
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@Yastiandrie is most likely right, your HP printer is still trying to use your old Wi-Fi network settings.
I also use this printer, and the easiest way I found to reconnect the printer was to do the following (reference: HP Article)
HP provides a more detailed process with screenshots on their website, which might be helpful if my steps above aren't that great. You can view it here: http://support.hp.com/au-en/product/hp-deskjet-ink-advantage-3630-all-in-one-printer-series/7172313/...