Printing disconnects online

Greetings,
I’ve used a printer hooked to my laptop for many years using the multi-pin connector, but recently switched to a newer printer with a USB hook-up. Now, when I’m printing something online, my regular phone line modem disconnects me shortly after the printer starts printing. I contacted HP and they gave me a couple things to try, including reinstalling, but it still does it. What’s up?
Thanks,
Don