Hey Mrinal. Well even I stay in India and I have been using an unlocked SGH-I777. My display has been cracked but ts still working as perfect as it was before.
Well about your issue, I can say is even if you flash a I9000 ROM, you may get the home button to work, but you will have to use the default kernel which comes inside the ROM itself. But as it is meant for the I9i000 you may face certain problems(software related) if you use it on SGH-I777.
So all I can say is if you are okay with the issues that may be faced, go ahead and give it a try.
And please let me know how much did they charge you to replace the display.