How do I get iTunes songs off the iCloud back onto my computer, preferably without changing the purchase date to today's date?

Question

Trying to download previously purchased iTunes songs that are firmly embedded in the iCloud. At one point these songs were all on my computer. Then I idiotically joined iCloud. All the songs were sucked off and into iCloud. iCloud couldn't provide more than twenty seconds of any song without freezing whatever device, Macbook Pro, iPhone 4s, ipods, or breaking up the playback into fits and starts and finally silence, ever, no matter if the connection was cable or wireless.
I have ever update on every device, I have the max. RAM, excess disk/flash space. The problem is the difficulty of downloading. Oddly the download to my ancient PC went almost without a hitch, it is with Apple devices that the trouble lies.
About 2/3 of the songs have successfully downloaded to my computer. However the purchase date, which I used frequently as a search/sort function, have on many of the songs been switched to today's date, or the date of the latest download instead of my original purchase date.
Many songs downloaded, many remain in the cloud with the 'cloud' icon beside them.
Clicking on the "download all" icon doesn't download them all.
They begin to download and then stop/freeze.
I'm reduced to manually scrolling to each song and clicking on the 'cloud' to download, this works sometimes and sometimes it doesn't. The whole thing usually crashes after a while.
This is where I am now, at the iTunes store on the "Purchased" page with all my songs in a list with "downloaded" or a "cloud icon" in the far right column, frozen once again.
I really would like to maintain the original purchased date(the day when I purchased the song from iTunes) but I'm to the point where I'd just be happy to get them downloaded onto the Macbook Pro, and hopefully never deal with the cloud again for the rest of my life.
Lastly, if anyone can recommend an alternative music site to iTunes it would be welcome.
Thank you.

Answer 1

I copied the iTunes file from the external drive and it's in both places.  I thought all I would need is the iTunes program (which I downloaded to new computer) and my iTunes library file.  There must be something else that's missing.  My iTunes library looks the same on the new computer as it does when I open it on the external drive.  If I click on an iTunes library song from my new computer, it will only play if I have the external drive plugged in.
My back-up drive is a mess.  I have multiple copies of music, video, photo, and document files and I don't know how that happened. ={  Obviously, I don't know how to back up stuff properly and there are back-up files extending over a 6- to 8-year period.  I think all I did was just drag and drop the main folders from the back-up drive to the same main folders on the C: drive.  Also (and I'm kind of fuzzy on this) Windows used to automatically save music files in a folder within my document files (which makes no sense to me).  As my Jewish friends would say, "Oy Vey!"