If your LAN card is not working:
Open caninet, and change the PCI slot of LAN card. Start your system, new hardware will be found.Let windows find appropriate driver.
If you have onboard LAN card.
Go to device manager, find any ? mark in network devices.Update the drives online or provide motherboard CD
regarding using USB for connecting your DSL modemFirst, I will never recommend you to use USB interface.USB has common problem of frequent disconnection.You need to jack out and in USB cable after every 15-20 min. And it has no solution.
Now regarding USB driver.
1) Request BSNL to change modem.They should do it for free.When I was at Airtel BB, I use to change hand to hand.

2) Upgrade firmware of your modem.Than you can install Vista compatible driver.
3) Buy a new modem, and let BSNL keep its rented modem.