You may want to try disconnecting then reconnecting the coax cable wire from the modem while you wait the minute during the powering up procedure.
Also, some cable modems will have a "reset all defaults" or similar button. This button is a virtual one on the Motorola modems. If your modem doesn't have that feature, and the above suggestions don't work, I would try leaving it unplugged for a few more minutes then powering it back up.
My bet is that your modem is remembering old settings and is confusing the router when it tries to connect.
Worst case scenario is that you may have to reconfigure your router. It could be that there's some corrupted settings there.
Edit to add: My Charter cable issued UBEE is very forgiving with routers in that I don't have to power cycle it but my Motorola SB6120 is not quite as forgiving. Sometimes it requires a restart and sometimes it doesn't.