part in the sliding slot of a casement window

It looks like you're showing us pictures of a coil balance window for a hung window. This isn't a casement window, though. Can you confirm that these are the right pictures? If not, could you try uploading them again for us? 

Ah, okay. That's good news, it'll make things a lot easier. We can definitely replace this hardware. When it comes to coil balances, the best way to identify what you have is to go by the pivot shoe. This is the rectangular or square-ish block of plastic to which the spring attaches. It will have a round center cam, as well. You can see our entire selection here for reference.

Basically, the pivot shoe acts as a "key" for everything else, in terms of identification. If I can see a picture of it, I can tell you everything you need to repair the balance.

They sure are! This looks like our 15-191 pivot shoe, which is commonly used with our 1/2" thick Series 160 coil spring. Looking at your first set of photos, the style of your old springs does appear similar to our Series 160. Look it over and let me know what you think!

Keep in mind you only need to replace what's broken. If the springs are the only damaged part of the balance, you can re-use the rest. Assuming you need everything though, take a look at our 15-150D or 15-150T cover (depending on how many springs you use per side, I can't tell) and 15-148 bumper.

You'll need the stamp printed on the old springs to confirm what Series 160 option to order. If you can't read the stamp, let me know the exact weight of the sash and how many springs are used on each side and we can work from there.

I'm afraid we don't have a cover exactly like yours. As long as you have the 15-191 pivot shoe and a 1/2" thick Series 160 spring, then the ones I recommended should work fine.

I'm a little confused about the stamps you need. Are these three springs all used on one side of the sash? Please confirm and we can work from there. If these are just the three on one side of the window, I'd like you to confirm the weight of your sash. If it's only 17.25 pounds, then your springs would be too strong. Having a 5.5 pound spring and a 3.5 pound spring on each side of the window would exceed your given sash weight (9 pounds on each side, totaling 18 pounds of total support). That's not even counting the mystery spring with no stamp, which would push it even higher.

I'm afraid we are not able to sell these parts in one complete kit. 

You're welcome. Let me know if you encounter any problems.