India isn't closed for colonisation- South India might be but there are all those states in the North.
The main thing that changes is that over the next hundred years or so, as the Infantry Revolution spreads across India, Europe is going to lose it's technological advantage. What with conflict within India it might well be Indian armies that begin to make more breakthroughs in military science- perhaps linear formations or Napoleonic columns or bayonets might be invented by Indians ITTL. This is going to make life more difficult for colonialists ITTL but at this point in time (early 17th C) there's no reason trading posts at the mouths of the Ganges and Indus can't develop into larger colonial establishments in future.
Also what do people think the knock on effects are going to be with South India relatively off limits (i.e. colonial profit is going to have to come from outright trade not occupation and institution of a plantation economy)? Perhaps an earlier more aggressive focus on the Malay states and Indo-China? IOTL these remained relatively ignored until the 19th C but ITTL things will be different.
Maybe also a greater focus on East Africa? Much of it has the right climate for plantation crops- spices or sugar could be transplanted in some cases.
The biggest effect will honest be that we may see a much more limited conquest colonism (the British control of India was quite inspirational to other power in the 19th century), and a greater focus on
factories and other economical outposts.
Economical I think this are going to mean that Europe are going to richer, through we may see Britain being relative poorer, mostly because we see the British middleman being removed, but also because a richer and more independent India would be a bigger marked for European products.
The biggest winner I imagine would be the Dutch, whose traders will continue having access to India for a longer periode, and may likely end up being the middleman for trade in the Indian Ocean (especially because they likely still end up dominating South East Asia).
Of course if India turn into a major consumer of imported sugar, the European will likely set up plantage colonies in East Africa, if not it likely stay much like OTL.
For the Americas the major different will likely be a relative poorer Britain in the 18th century, beside that it's unlikely we will see a major difference beside the butterflies.
If you decide to let the Danish be a bigger player on the Vijayanagara (would Europeans call it that?) marked, the result a richer Denmark, which will likely hit in the more agressive part of Danish history between 1660-1720, which will have massive effect on the Baltic and North Germany (especially because the Hanovers will likely be butterflied away). So we may see a Denmark which at the very least end up with Swedens and Gottorps German possesions (I guess the 30 Years War still end up much like OTL).