I understand that you have troubles setting up the Slingbox after changing your provider and the way to connect your equipment is not that complicated. The Slingbox needs to be connected to the Internet using a router and also to your TV source (DVR). From the wall you have the coaxial cable that splits to the modem and to the DVR, let's work first with the modem, you need to connect the router to it, and the Slingbox needs to be connected to that router. On the other side, connect the DVR to the Slingbox using the Audio/Video cables, you can use component, composite, S-video or coaxial. Then you just need to run the Setup at slingbox.com and at the end, it will work anywhere.
If you need more assistance connecting the Slingbox, have a look at this,
Hope this helps