Belkin print their model numbers on the sticker on the base of the router.
If I'm reading your post correctly it was working fine until the Windows install corrupted (for a, currently, undetermined reason). But since you reinstalled, Windows forgets the settings on shut down? If so go to device manager: [winkey]+[R] > devmgmt.msc
Navigate and, if needed, expand the Network adapters and Universal Serial Bus controllers entries. Are there any yellow triangles with exclamation points in them?