I may have this wrong but this is what it sounds like you've done
got a tank, filled it with water, decor etc and left it for 4 weeks
had the water tested at an un-reliable garden centre lfs
fully stocked your tank
then within a week everyone's ill and dying off.
Hate to say it but I'm not in the least bit surprised. Just leaving your tank for 4 weeks will do diddly squat to get the beneficial bacteia that the filter needs built up. Yes the stats probably were fine when the garden centre tested the water, there won't have been any amonia or nitrite as there's nothing producing waste so no amonia, and no bacteria colony dealing with it so nothing to convert it into nitrite or nitrate.
Your tank is now cycling, which is a very stressful process to put your fish through. If your going to cycle with fish you need to do it with just a few very hardy ones, not fully stock it, it's no surprise your filter can't cope.
All the fish will have been producing waste and therefore amonia, you've probably had the initial part of cycling which is the ammonia spike, this will have weakened your fish, then comes the nitrite spike, this is extremley toxic and is probably what has killed your fish and made the rest of them ill. You may still loose more fish.
If you can take any fish that are still well out of the tank and re-home them asap, any fish that are poorly I'm sure you won't be able to re-home, you may well loose these as well.
If you know anyone with a mature fish tank then get some filter media from one of they're tanks and put it in you filter, this should hopefully speed up the cycling and maturation process. At the top of the beginers section there's a post of TFF members willing to donate media, have a look if anyone is near you. Also I'd advise you read the thread about fishless cycling for future reference.
Invest in a good quality test kit. I'd recommend the API kit personally, test your water daily and do daily 20% water changes until your stats are
amonia - 0
nitrite - 0
nitrate - less than 40
good luck
