WILL Music on my Itunes Account automatically be on Itunes when I redownload it on a NEW PC?

If you purchased music from the iTunes Store, then once you sign into your iTunes Store account, you will be able to download those songs. But other music, from CDs, other digital stores etc. will not be there, it's nothing to do with the iTunes Store or your iTunes Store account.

iTunes, and the iTunes Store are two separate things: iTunes lists all the music you add to it, not matter where you bought it, while the iTunes Store is where you can re-download music purchased from there. The iTunes Store is similar to buying music from Amazon.

So, where do you go from here?

Well, first of all, is your music on an iPod, iPad or iPhone? If so, there are ways to retrieve the music from them but it is not straightforward. You cannot simply transfer music form such devices back to iTunes. The solutions that enable this will cost money (apart from a few free goes)*. Did you ever make a backup of your music, onto an external hard drive for example, or to online (cloud) storage? If so, use that. For any of the non-iTunes Store purchases that you are unable to find, you will have to resort to:

• • purchases from Amazon, or other online stores, go to your account with that store and download the songs again
  • songs directly from artist websites, go back to those
  • personal recordings - bad news, unless you have a backup, you've almost certainly lost them (unless you resort to the recover music from iPod route)

* If you want more information about recovering the music from a portable Apple device, read this article, from user tt2: Recover your iTunes library from your iPo… - Apple Community

For the future see Backup your iTunes for Windows library with SyncToy - Apple Community. Depending on the exact issue you may still be able to recover files from dead computer's drive if you haven't yet disposed of it.

tt2