Replacement balances
It looks like the bottom hook on your balance cord has just turned around the wrong way. With pliers, you should be able turn it back around so you can engage the balance to the window track hole.
As for what this is, I agree that our S385-27 looks like the right match. I'd also recommend the 2640 option.
Well, age alone can affect things, but you can try lubricating them. It certainly can't hurt, and it may turn out that that's all you need. Remove the balances and turn them over so you can see the open back where the spring and pulley are. Spray a lite lubricate oil on the spring, cord and pulleys to loosen them up.
I should also tell you..... the worst windows are the South facing side of the house. It was 8 years old and never lived in when my son bought it. He lives where they have extremely hot, long summers and farms almonds there. So, after the home was set up, it's been cooking in that heat for 4-5 years.
"As for what this is, I agree that our S385-27 looks like the right match. I'd also recommend the 2640 option." Am I correct in the difference is only the depth of the very bottom plastic clip?
Thanks again for all your help! I will be trying this out this weekend when I visit.
I wanted to add that the sun also plays a role in the life expediency of window parts. As for the oil for the spring and pulleys, use 3-In-One Oil. Don't use it on the window tracks; for those, you want silicone spray. It goes on dry and doesn't collect dirt.