I have been trying to index our website (www.mtbc.com) on google for
over 3 months now, but so far no luck, can you help and let me know
what am I
doing wrong or what is the problem with our website?

Thanks

My idea:

Since your site is so heavily Javascript run, and although you have
the META tag included, there aren't many keywords for Google to search
for in your website. Google doesn't search through META tags like
other search engines do.

Well, I believe google DON'T know the existence of your site :

Look at here :
http://info.alexa.com/data/details?p=TBChrome_T_t_40_L1&amzn_id=alexa65-tb-20&url=http://www.mtbc.com/

There is only 1 site in this world link to you. If google don't know that
site as well, there is imposible for google knowing you. You don't submit
your site to google. Google get to know you automatically through other site
which refer to you. If nobody refers to you or very few people refer to
you, most likely forever google don't know you exist.

Try to find way so that more people link to your site.

You can try to add your website to the Open Directory Project (dmoz.org)
I think it's simplest way.