The reset part is easy (button on the back next to power connector). That, however will probably wipe out your wireless settings and they will have to be redone. If you're not using the wireless part, everything else should work fine. If you are, there are a couple of options:
Hook up the router, go into it (see manual link below) and save the settings. You don't need Internet for this, just a direct connection from a PC to the router. After you reset the router, go into the router again and restore the settings you just saved.
Don't save the current settings. Reset the router and using the manual "start over" from scratch.
I assumed you tried a "soft reset" of just powering doen both the TWC modem & the Dlink and just restarting both of them.
Link to manual:
http://static.highspeedbackbone.net/pdf/D-link-DIR-655-Manual.pdf