I am going to install D-Link Broadband WiFi Router. I have to place the router in my drawing room. I want to connect my 3 Computers, which are situated in three different rooms and those are not in line of sight (LOS) with the broadband router, through wireless. Is it possible to communicate between computers and routers through WiFi if they are not in LOS? How much distance can I place them to communicate is they are not in LOS?

Yes as Wireless uses RADIO waves and doesn't need LOS at all.
Admittedly to many walls/floors can degrade the signal.

Wireless can travel through walls, for this reason, you should also be sure to secure your network. As far as distance, I work in a warehouse that is pretty well wide open. To maintain a strong connection, we place Access Points every 100 feet or so. This produces a bit of overlap, but keeps a strong signal. I would estimate that a Wireless G router centrally located in a home should be able to cover at least most places in the house.