Then you need a WiFi Client device.
Some call it a bridge but the router you had, did not do the client mode and same for your Belkin.
I've used TOO MANY so without further ado, cheap bridge?
Under 17 bucks in 2 days to my door. Hard to beat.
WARNING. Some folk will complain it drops when you hide your SSID. Yup. Most things will drop like that.