I've put off answering this because I'm 'fraid I have little to no experience with cable modems/DSL modems/etc. I have a book or two around somewhere (and the Internet, of course), but I've never had to set up my own equipment, enter my own settings, or anything like that. However, if you are consistently getting good speeds when you have connected directly to the modem, then I believe the settings on your cable modem aren't your issue.
I am assuming you've already tried all the obvious stuff to make sure it's not just a bad port, bad cable, that sort of thing. So here's some things to try:
-Make sure the cable company knows the MAC address of your router. Some ISPs will kill your connection if they don't recognize the device that's plugged into it. Give them a call, explain that you just switched your router, and ask if they need to know your new MAC address. Your computer works fine, but they may already have your computer's MAC whitelisted from previous.
-Find out whether or not the cable modem is giving the device plugged into it an IP address in the private range (starts with 192, 10, or 172), and if so, make sure the addresses that the router hands out to all the devices connected downstream from it are not in the same subnet. On a related note, if you are using WiFi, use either the router wifi or the cable modem wifi, but not both. Turn WiFi off on the device you aren't using.
-If your router has more than one LAN port, disable DHCP on your router, and then plug the connection from the cable modem into the LAN side of your router instead of the WAN port. This will transform your router into just a hub/switch. If speeds magically go back up to normal, then you have a routing issue, not a device issue, and you will need to find out what is up with your routing layout.
-There's a chance that the issue is just that you have too many splitters in your cable line. Routing your signal from one main cable line to 4 different cable boxes will cut your signal down quite a bit. If your slowdowns happen when everyone is watching cable (especially digital channels), then that's probably your culprit.
Also, the image link in the OP is broken.
--Patrick