How do I save money on this iPod repair?

Hi Henry,

iFixit has guides for your repairs, which I'm sure you're aware of. I've worked on these little puppies and I have to say, they are somewhat difficult to work with. It is doable, though, but be sure to take care and follow the instructions to the letter.

iPod Nano 4th Generation Display Replacement - iFixit Repair Guide

For your screen replacement, parts are readily available; I found one on AliExpress for a whole $9 USD, plus shipping.

Internal LCD Display Screen Repair Replacement for iPod Nano 3rd 4th 5th 6th 7th 4GB 8GB 16GB - AliExpress 509

LIkewise, batteries are quite inexpensive too; here's one for under $4, but with shipping you'll pay around $10 total.

Replacement Battery for iPod Nano 1st,2nd,3rd,4th,5th,6th,7th upgrade nano battery - AliExpress 509

Unlike most other Apple products, the battery wires are soldered on and soldering experience is needed to replace it, so be forewarned.

iPod Nano 4th Generation Battery Replacement - iFixit Repair Guide

I know some of my colleagues disdain AliExpress and eBay, but those are generally where you'll find the cheapest parts. eBay tends to be a little more expensive than AliExpress, but the shipping times are generally shorter. Of course, there's always Amazon; you can get stuff quick but you may pay a little more for that convenience. I've bought quite a lot of parts from those sites and generally have had good experiences with them. But that's just my personal opinion; take it for what you paid for it. :)

Of course, should you wish to support iFixit's repair efforts, you can always buy the parts from them; the battery in particular isn't too costly.

iPod nano (4th Gen) Battery

Whatever source you choose, you'll definitely want to do both repairs at the same time; if you can help not disassembling the darn thing twice you'll be thankful.