They know what you purchased from the iTunes Store and you can re-download everything you purchased. Whatever you bought is yours to download as often as you require, as long as it is still available in the Store.
Here is the procedure for your reference when you replace your computer.
On your replacement computer, launch iTunes. Click on iTunes Store on the left
On the right you will see something like this
"Sign in" using the Apple ID used to purchase your songs, then click on "Purchased" (with the orange blob)
On the summary page that appears select the tab "Not on This Computer" on the right.
On the list that appears, select what you want and then click the "Download" button.
When you want to play your newly downloaded music on your replacement PC, you will have to "authorize" it. Don't worry about the dead computer until enough of your computers crash that you reach the limit of 5. Then you can "deauthorize all" and re-authorize as necessary.
Downloading past purchases from the App Store, iBookstore, and iTunes Store
Thank you so much Mr. Galt. (Love the moniker) As every thing is going to tablets and phones, etc. I thought to update my media. This is a Chromebook. Not what I thought it would be for it's way too easy. All the same the formats and protocols are worlds apart from my beloved PC... A slow, learning-as-I-go process. I will try to download itunes but the chromebook has a separate program (app...) for this. Thank you again for your prompt and informative response.
Sandy Sowards Hinderer
... This may be more difficulty than it is worth.
The Chromebook fills a niche, probably one left vacant by the "netbook" efforts of a couple years ago, but it falls considerably short of what I need a computer to do.
$200+ for a dedicated web browser doesn't excite me. Considering that Google derives nearly all its revenue from advertisements they really ought to be free.