Okay, a couple of important preservation things first off - use Calibre as your ebook library manager, and immediately you buy an ebook, in any format, and have downloaded it either in ADE or Kindle for PC, import it into Calibre using Alf's Tools.
Here is the link to Calibre:
http://calibre-ebook.com/
Here is the link to Apprentice Alf:
https://apprenticealf.wordpress.com/
You will likely need some help, so go to the Calibre forum within MR
https://www.mobileread.com/forums/forumdisplay.php?f=236
Ask for help in Alf's comments section:
https://apprenticealf.wordpress.com/...sted/#comments
Okay, with respect to getting at your pdf ebooks, do you see them on your Kobo ereader? (Which ereader do you have btw?)
If you can see them and open them on your ereader, then you will be able to import them to Calibre, where you will be able to convert them if you want.
And I agree with you re Kobo not being able to download your PDF's - that is a Kobo issue and the Kobo help desk should be able to address that. But, I'm assuming that you can still see them in your kobobooks.com Library?
Also, go into your Purchase History because they will be in there if Kobo wants further evidence of your purchase.
Good luck - I've gotta dash out (well, Mothers Day here and all that!).