While it's not impossible for you to make it into a top business school programs, it will be much harder for you.
I think that if there's a will, there's a way and if this is truly what you want now (and know why you want it), start looking at some schools that will help you get to where you want to be. All schools publish their employment data, with most schools publishing top employers. See if there are any employers on anyone's list that you may fancy working for. With some luck, it's definitely doable. (And remember, sometimes things just don't work out as you planned not because of a lack on your part, but simply a more risk-aversed adcom reads your application)
One thing I'm a bit confused about is your saying of EMBA. You don't want to attend EMBA because your company doesn't sponsor it. Can't you still go for it by taking out a loan? Pardon my inexperience in the EMBA path but I thought you could still take out loans to cover for your tuition in the EMBA route. (Finances aside, I do think an EMBA will benefit you with a much higher return than you'd benefit from a tradition fulltime MBA)
GMAT Club Premium Membership - big benefits and savings