My coputer died and now I have no access to my tunes. Does Apple itunes have a record or file of my library?
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