New ignition lock cylinder on 2002 Saturn SL2

My daughter's key will barely turn the lock cylinder. Sometimes it takes quite a lot of wiggling to get it to work. I bought a new one from autozone online. It said it was the lock cylinder and keys. When it came, it was a cylinder with a bunch of little metal "H"s. I would call them the tumblers. (but clearly I don't know what I'm talking about) There are 4 little bags, bag 1, 2, 3, 4 all have what appear to be 5 each identical little metal H's. Bag 10 has 10 little springs. I went to auto zone to help. He put the key in the cylinder and slid a # 1 into the cylinder down the row until he said, "see there, it slides all the way in, so this slot gets a one. Now just go down the row and see which number each slot gets." I got home, and ALL THE H'S SLIDE ALL THE WAY IN, if you take a paper clip and just seat them snugly, they all look identical. So, how in the world do I set up this new cylinder to work with her key? I have exhausted myself looking for advice and videos online and have no where else to turn. My next step is to return this cylinder, get my money back and buy one from a salvage, that is probably almost as worn out as my daughter's. Thanks in advance for your help!

Asked by for the 2002 Saturn SL2
Do you still have the original lock cylinder? that would be very helpful and you could possibly re-key the new one to match your original keys.