I'm sorry about your new koi. Why would they die and not the goldfish? It could be that the koi carry some disease that was more advanced on them and might eventually get to the goldfish. It could be that the koi were too beat up or unhealthy when you got them although it sounds like they're fine. It could be that the koi have something that goldfish don't get like the KHV. It could be that the koi died because they are more sensitive to certain things than goldfish such as low oxygen.
Your pond pH should ideally be between 7 and 8. If it's much above 8, you need to figure out why and try to bring it down. I suggest getting an accurate reading of the pH. The store only tested for certain things. What did they test for? Ideally, you would test for pH, hardness, alkalinity, ammonia, nitrite, nitrate, and oxygen levels to start with when a problem is afoot. What kind of filtration and aeration do you have?
Check out this web page:
http://www.koivet.com/There are pages on that site about Koi Herpes Virus such as
http://koivet.com/html/articles/articles_r...search_term=KHVIf you suspect KHV, it might make sense to take the koi out and heat them to 87 degrees F to kill the virus. I am not sure if the entire pond has to be heated, if the virus is in the water or carried by goldfish. The site probably tells you somewhere. If it's KHV, you can expect to lose the rest of the koi eventually.
You may not be able to have the koi tested by an official lab but I do suggest contacting your local koi club. They will often come out and put the fish scrapings under a microscope and be able to diagnose many of the basic problems that koi can have.
Koi experts say to have 1000 gallons for the first koi and 100 gallons or more for each additional koi. So, in the end, I suggest onyl keeping a few koi in your pond anyway. I wouldn't add any more koi. If your three survive, hopefully, they will be plenty.
Sitting on the bottom (lethargy) can be a symptom of almost any parasites, bacteria, fungus, virus, etc. They could have gill or skin flukes. Flukes would also infect the goldfish.
Adding salt to the pond helps with my parasites, bacteria, funguses, etc. but not viruses. If you have plants, keep the salt concentration below 0.05%, or the plants will start to yellow and die. In a plant-free pond, 0.1% salt can be used.
I suggest trying to contact your local koi club for help (to look at scrapings of the fish under a microscope which will tell you if they have flukes, etc.), testing the water for a wider range of things, continuing with partial water changes, filtering and aerating the water well, adding some pond salt and maybe some MelaFix, adding parasitic killer only if that problem is verified (or pretty likely; parasitic medications can kill good bacteria, sometimes tadpoles, snails, insects, weak fish, etc.), and waiting.
I hope things improve!