Landline Not Working Properly When BB Cord Plugged In

I am facing a rather strange problem. I am using ZTE ADSL 831 Mode. My BB seems to working fine. But my landline is behaving strangely as long as the Modem's cord is plugged into splitter. I am able to make outgoing calls but I am not able to receive any incoming call. On being called there's just a faint crackling sound at the end of caller instead of the usual ringing. The landline doesn't rings at all.
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However, the landline works fine if I remove the modem cord from the splitter. The BSNL linemen are completely clueless about the situation. Please help!

It is most likely your splitter that needs replacement. Borrow one from some one to check if that resolves it and if it does go buy a new one. They are pretty cheap.

I tried that, but the problem still persists

It has something to do with the Bsnl exchange. You cannot do anything about it yourself. Complaint to Bsnl in writing.

Contact BSNL and make a complaint about this problem and someone should come and fix the problem, its probably something to do with the wiring end.

Its a back end problem that needs to be sorted out from BSNL's side.

complain to BSNL, and ask them to get their lineman out to your place.
ask him to check at the pole DP if there is a similar noise.
ask him to check at the exchange at the jumpers if there is a noise.

this will help you to isolate the fault, and place the blame.

change the filter on your bb line. Not just a splitter, but an ADSL filter. It filters out the high frequency DSL signal from the cable, and gives you a cleaner line.
do you have a wireless phone? disconnect and turn it off, and connect a regular phone to the line and see if that improves the line noise situation.
see if that wireless phone or a microwave oven are causing issues with line noise.