Are there any famous traditional festivals in the west side of South America in March/April ?
I'm referring to Peru, Bolivia, Chile, Equador, maybe Paraguay.
For example, I've found out in Lima, Peru, there is the Huaylarsh in March.
As we pointed out in some comments, there really are tons out there. It being mostly a Catholic (historically) and Spanish-Portuguese continent, a lot of the festivals tend to be related to dates at similar times, as well as historical dates (independence days and the like).
For this, I'd recommend a site like Festivals in South America - which lists around 70 well-known festivals. Then they have a sorting tool on the right which will let you sort by country, month and the like.
Unfortunately you're a bit late for Carnaval and a bit early for Boi Bumba, but there are plenty others in that list in South America in the months you mention!
Most festivals are in spring and summer over here (Chile), starting in September until early in the next year (Jan/Feb).
March and April are the first off-season months (all schools are open again and tourists have left). The weather is still very good (speciaal voor ons Nederlanders hehe), and another positive thing is that the prices of Hotels or Hotel Apart, or Cabañas are at their lowest.
But for festivals you're pretty much in the wrong season of the year!