[johnwill]

Try power cycling the modem when you connect directly, that's a required step. You need to isolate the issue to either the ISP/modem or the router.

 

[johnwill]

When you're directly connected to the modem, do this:

Start, Run, CMD to open a command prompt:

Type the following command:

IPCONFIG /ALL

Right click in the command window and choose Select All, then hit Enter.
Paste the results in a message here.

 

[johnwill]

If you have slow connections with no router, clearly, that's an issue that should be addressed first.

I think it's time to call your ISP and hold their feet to the fire.

 

[johnwill]

Upgrade the firmware on the router, do a factory reset of the router, see if that helps.