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...will connect EITHER through the USB or the Ethernet port but not both. You probably would need to reset the modem in between switching from one to the other.

So you've switched to a cisco?

The router probably is supplying an IP address to the DVR (and any other devices connected to it). Cycling the power on the router may change any of those addresses. You probably have port forwarding configured to point to a specific IP address to access the DVR from any PCs, smart phones... This won't work if the DVR has been given a new IP.

Your router probably has the option to reserve an IP address which is what I do for my networked printer/scanner/fax. It will always get the same IP. If you give me the model number I'll try to find you some instructions.

...to the router's User Guide: http://homedownloads.cisco.com/downloads/userguide/1224694474459/EA-Series_UG_Full_3425-00125C_EN_FR-CA_Web.pdf

Page 39 has the instructions for adding a reserved IP. There's no way for me to tell what you should set that to. You'll need to look at page 51 to see how to access the port forwarding settings. The IP to which the port is forwarded is the IP you need to reserve for your DVR.

Hope this helps.

Thanks!