dhanchey, I had the same problem. My static home page was perfect until I started messing with the reading options. Here’s what you can do.
There seems to be a bug you can exploit. Name your static home page. Any name will do. Make it into a static page through reading options as described above.
Then go back and edit that page, delete the title and add a space (I added three spaces and it works).
That’s all! The title of the page is still displayed but it’s just space(s) so it’s invisible.
I’m using 2.3.2 but it worked in older versions too.