Hmmm ... my idea for the subnet mask is gone now. For the start, you could use the Belkin router for internet connection and the Linksys router as switch if it has a feature "Connect to internet via LAN" (means the Belkin handles the DSL connection and the Linksys just works as switch, attached to the Belkin).
You didn't mention the exact model of your Belkin router so I can't look how new the current firmware is. Maybe it's a pretty new model and the firmware still in "End-User testing state" (pretty common these days).
Unfortunately, I can't figure out if the LAN ports of the Linksys have fully auto-recognize feature (means you can connect a LAN client via 1:1 or cross-over cable) and the Belkin has not.
I remember myself you had established a direct connection to your PC, what means you connected two "LAN client" ports together. This is only possible if you use a Cross-Over cable or if the PC LAN port has Auto-recognize feature (which is NOT common). This lets me assume you had (or maybe still have) a cross-over cable attached to your NAS, when you established the PC connection.
You can check easily if it's a Cross-Over cable: hold both connectors to each other, facing the contacts side into the same direction (not vice-versa) and the transparent side up. Then compare the color order of the single wires in the connector.
- If the color's order on both connectors are the same, it's a 1:1 cable which is recommended for connection to routers.
- If they have different color orders, you have a cross-over, which are made for PC-to-PC connections w/o router or switches.
If it's a cross-over cable, replace it with a 1:1 and try the connection NAS <--> Belkin again.
//HSishi