Did you cycle the tank, that means keeping the tank with the filters running and let it sit without fish for about 2-3 weeks??
Because if you don't I will be quite shure all your neons will die. When you start up a tank, the water won't be good enough to add fish yet (it has chlorine -spelling?- and stuff in). This has to do with bacteria witch make the water good for fish to live in and break down the waist in to less poisnes substance (witch you removes by doing water changes. They need some time to grow untill they can "solve" the waist of fish.
When there are no bacteria the waist of the fish begins to pile up and creates an toxic enivroment for the fish, they are basicly swimming in there own pee.
There are some ways to speed up the cycle, buy bacteria and add to the water to kick start there grow or add some from a tank wich has been up and running (healthy) for a longer periode.
But for now, you might wanna get the fish out and bring them back to the store or get a lot of easy and fast growing real aquatic plants (when you get them above the water they are weak, unlike anubias or so). The reason for this is that the plants help to break down the pee and if there not so many fish it may help.
Good luck!
Loubard
P.s. With Eheim is it gonna be? Is the Eheim filter gonna be the only filter? Then you need to make shure the filter works both mechanical (to filter out the poo and food leftovers) and biological (to house bacteria that break down the pee and lots and lot more).
First add some foam (not the fine one), then some bioballs and then 3 cm of fine foam.
@Dead-N-Dreaming: hope you already knew all this written above. And else it's a good learn; I hope..that is.

Long story, if I am wrong somewhere; please correct me.