EDIT:
The problem is definitely with Adobe. They have this thing called DRM (Digital Rights Management), that's essentially a layer of protection that's supposed to minimize the amount of book piracy. Essentially, when you buy a book with DRM (as opposed to DRM-free), you are not downloading a .PDF or .EPUB file, you are getting a .ACSM, which is Adobe's file format for license + book. So if you open that .ACSM file with an Adobe-supported app (such as ADE), it can figure out whether the license is valid or not - in other words whether you've purchased the book yourself or if you've just downloaded it from the Internet - and if it is, let you read it.
The downside is, obviously, a situation like yours, where you simply want to read the book on a device that doesn't know how to handle .ACSM files. Unfortunately, there is no "proper" way to do this, you need to get rid of this license Adobe attached to your book and work with an actual real DRM-free PDF. If you google something like ".acsm to pdf" or "remove DRM from .acsm file" you should be able to find plenty of tools online. I'll link to just one of them - but keep in mind, I haven't tested it myself. http://www.epubor.com/how-to-convert-acsm-to-pdf-free.html
Take a look around either My Documents or your AppData. You can find the latter by pressing {Windows Key}+R to bring up the Run window, and then typing %AppData%. This will probably send you to C:\Users{username}\AppData\Roaming, but if you can't find a folder called Kobo Desktop or something similar, you may need to step up from Roaming and take a look at Local.
This being said, from what I could gather online, it may be damn near impossible to do what you want to do without stripping the books off their DRM.