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Okay, somehow or the other, I got it to work using tips gleaned from various links from Googling 'brand new Galaxy Nexus not booting'. I haven't figured out the issue, but I had the phone plugged in without the battery and inserting the battery then showed me battery charging image on the phone for the first time, but it quickly died out and I couldn't start the phone. After subtly pressuring the battery randomly, I got the charging screen back and switched it on.

Some of the posts in the aforementioned Googling suggested there might be slight defects in the Chinese-made Galaxy Nexuses (apparently it was made in both Korea and China), and mine is made in China. It might have to do with the battery not getting placed just right. I suggest to anyone facing similar issues to try to see if there's any effect with inserting the battery with the phone plugged in as I did in my case.