Should I go fish my old modem out of the trash?

After a couple of days on the phone with ATT, trying to get my internet connection to work, I decided to hook up a new modem. I thought that would fix my problem, but after an hour or so I lost my connection again. So, back on the phone with ATT again, for hours, I hope this fix lasts longer. Should I go fish my old modem out of the trash?