How can I make my neural network emphasize that some data is more important than the rest?
To emphasize on any vector elements in your input vector you will have to give less information of the unimportant vector to your neural network.
Try to encode the first less important 285 numbers into one number or any vector size you like, with a a multiplayer neural network then use that number with other 4 number as a input to a neural network. 
Example:
v1=[1,2,3,..........285]
v2=[286,287,288,289]
v_out= Neural_network(input_vector=v1,neurons=[100,1]) # 100 hidden unit with one outpt.
v_final=Neural_network(input_vector=v_out,neurons=[100,1]) # 100 hidden unit with one outpt.
I looked around online but couldn't find anything, but I may well have missed a piece of literature on this.  I am running a basic neural net on a 289 component vector to produce a 285 component vector.  In my input, the last 4 pieces of data are critical to change the rest of the input into the resultant 285 for the output.  That is to say, the input is 285 + 4, such that the 4 morph the rest of the input into the output.
But when running a neural network on this, I am not sure how to reflect this.  Would I need to use convolution on the rest of the input? I want my system to emphasize the 4 data points that critically affect the other 285.  I am still new to all of this, so a few pointers would be great!
Again, if there is something already written on this, then that would be awesome too.