Finally received dvi hdmi cable from ebay today. My current os x works fine after putting this, so means tested ok.
But I tried to boot with my Mavericks Usb and again after a point the monitor sleeps. So I tried to understand your next step mentioned but
Did not find any nvd* kexts in my installer drive (no kexts starting with name nvd). What do you mean by Original GM kext???
I mean the nvd*.kext from Apple store version of Mavericks. You have to install all of them.