Valor Telecom? Wow, that's a name I haven't heard for awhile. We did some contract work for them back in the day when they were just starting out. Their Windstream successor is, if anything, in even more disarray than they were.
One way is to choose a place in your home for your router, and run all the cables from each of the jacks to that location ("home run" them to your router location; one cat5 for each jack, no daisy-chaining). You could also run a new cat5 from your NID to your router location (if your current cable isn't long enough) and have the Windstream guy tie it into the NID instead of fixing up your old cable (assuming he shows up). Put a male cat5 connector on each of the cables near your router, then connect up your modem as it is now. If by chance your DSL router has enough Ethernet jacks for your homerun wires, then plug them in to your router and you're done. If not, buy a simple unmanaged Ethernet switch and run a cat5 cable from your router to the switch, then plug in your other homerun wires to the switch. You wouldn't need anything more than a 10/100 meg switch, since your DSL bandwidth is probably not all that high.
If you're only using the Internet and not the wireline telephone, then you don't need the DSL filter. If you want one anyway, Windstream should provide it.