Don't get a new filter! Or at least don't throw out your media. This is where all the beneficial bacteria lives. You only ever rinse the filter media out in tank water and never remove it or replace all of it at once as otherwise this will destroy your cycle.
It looks like your tank is cycled based on the readings you have, although the low nitrate is strange. Usually in a cycled tank you would expect to see more.
Can I ask how did you acclimatise your new fish, and do you have any readings for pH or hardness? Neons are softwater fish and so if your water is very hard with a high pH and they weren't acclimatised correctly, they may have died from the shock of the transition.
Otherwise, they might have just been sick in the store.