Presume this means you have changed the cable connecting your modem and PC.
3. LAN card is the socket where you plug in the ethernet (RJ45) cable from modem.
4. Changing modem's password won't affect the connection. Try GDMT as mentioned in other post.
5. I see a box before splitter, hope it is just the receiver box to which the line is connected from the BSNL junction box and no other connections are taken from the box.
6. Did you try connecting the line directly to the modem bypassing the splitter ?
7. May be the splitter is faulty, replace it and check