Is this what your after?
First post, be nice!
Columbus makes it to the new world, but doesn't make it back to Europe (Whatever method you like here - killed by natives, ships sink in cariberean reefs, Disease, Doesn't feel like it...)
As a result, European monarchs choose not to fund any further expeditions west fearing another Colombus like failure. However, because Columbus makes it to North America, so does European diseases. This causes much turmoil in the Americas as many rulers die of these diseases (like how smallpox (atleast it is thought to be smallpox) killed Huayna Capac which caused an Incan civil war). That should delay European colonisation and give the American population a higher degree of immunity to western diseases.
Reconquista as many have pointed out - would probably continue into Morocco. During these conquests, conquistadors hear of "the golden city of Timbuktu". These conquistadors then go on to take the Songhai empire, areas along the Niger river are then farmed, surrounding areas are used to produce sugar, cotton etc. The local populations are used to as labour on these farms/plantations.
The Portugese continue to focus on India/Indonesia area of the world. Eventually the "roaring forties" leads to the discovery of Australia (atleast Western Australia). Rather than hitting the Simpson desert quite a few Ships hit the South West area (South of modern day Perth) to find an area appropriate for farming. As many ships hit this part of the coast - it is thought to be larger than it actually is.
There is increased focus on colonising India, South Africa and Indonesia now as Europeans see how rich Spain and Portugal have become. The Dutch break free of Spain and following the Iberian Union the Dutch take control over the majority of Portugese colonies. England and France focus on colonising SE asia/India, India gets divided up between various European powers and a surviving Mughal empire. It is about this point in time that Akbar the great comes to power. Akbar, seen as a liberator by the Indian populace, gains wide support and ousts European political entities from the subcontinent.
So this leaves Europe with SE asia (probably struggling to assert supremecy), Indonesia (largely Dutch), South Africa (Disputed) and Western Africa (Spanish). The kingdom of Denmark-Norway, having laid claim to Iceland and Greenland, looks further West, to the "edge" of the world. Eventually they "discover" the "new world".
Now, moving onto what could happen during this time in the Americas...
The Aztec empire temporarily becomes smaller as Tenochtitlan would be a rather large city which means it would be severly effected by new diseases. However, this is only temporary, as the Aztec retain its farmlands, producing lots of food, producing a larger populace. Taking advantage of Maya disintegration they expand Eastwards, however this also allows the Maya city-states of Ko'woj and the K'iche' kingdom of Q'umarkaj expand and halt the Aztec forces. However, Aztecs require the gathering of slaves to sacrifice, so they continue to war, however this puts incredible strain on the Aztec economy and eventually the Aztec empire disintegrates.
When Huayna Capac, the leader of the Inca (sapa inca) dies suddenly of one of disease, civil war ensues and as in real life Atahualpa "wins". (As happened in real life, as disease suddenly killed Huayna Capac causing the civil war which Atahualpa "won", then the Spanish came...). Atahualpa, being an ambitious militaristic person as he was, continues to expand the empire. They look again overseas (and also assume Túpac Inca Yupanqui did indeed go on a previous successful Pacific expedition) as they have by this stage met tough resistence/too difficult terrain to expand much more overland. They gain (or regain) control over Easter island, head West to (re)find Polynesia. However obviously not being able to control an area so far away they instead move to gain knowledge, leading to better navigational skills. Later rulers do consolidate the Andes, and build on the road system to the point where expansion is once again possible.
So Norway/Denmark is "first" to the Americas, but lacks funding/people for alot of colonies. So they create a few small colonies then rely on good relations with natives (particually the Iroquois). Portugal under the Iberian union doesn't figure now, Spain by this time has mismanaged its economy so much that expansion is very unlikely, leaving Great Britain, France, Dutch, Norway/Denmark, Sweden to colonise the new world. They mostly focus on North America and gradually move southwards. There is a new wave of disease brought on, however it is not as devasting as disease was in reality.
France and Great Britain put aside their differences to "block" Other countries from establishing colonies in the new world. The Dutch, having control over Indonesia for some time now, effectively buy their way around this "block". France and Great Britain do this until tensions in their competing colonies escalate to the point of war but don't ask me who would win...The Dutch focus on consolidating trading posts, and open a trade route to the Incan Empire through current Panama and Colombia. Sweden has their colonies starved to death or conquered. As "revenge" they choose to invade Denmark/Norway who after seeking Iroquois assistance, manage to get their colonies to survive.
Now I'm out of ideas...mostly because we have two important wars going on - France vs Great Britain and Denmark/Norway vs Sweden. Would Russia join Denmark/Norway to defeat the Swedish threat? Also a potential alliance between the Dutch and the Inca. Would Portugal try to take the poorly managed Spanish colonies or choose to colonise Australia? Basically there are too many variables now...