DO NOT DELETE your Logic app. If you do you'll get an awful surprise from Apple because they will not allow you to download your older version of Logic. They will only let you download the most current version, forcing you to buy a newer computer. And deleting and reinstalling Apple programs does not reinstall all the additional items needed if you didn't delete those too.
If you want to try to reinstall the sound library. Quit Logic. And empty your OS trash.
In finder go to your hard-drive>Library>Audio
Here you will find your Apple Loops folder. These are the loops found in your loop library. If you aren't having problems with the loop library, your can leave that alone. Or you can delete it and rebuild them back in Logic.
You'll also see a Plug-in folder. Open that and most of the aftermarket plug-ins will be in VST(s) or other named folders. You can delete the unvalidated ones.
Now go back to the HD>Library>Application Support
Here you will find the Logic folder that has all the Sound for instruments. It can be pretty large depending on what you have downloaded. Mine is over 60GB. You can delete the whole folder or open it up and just delete the folders for the instrument that you haven't been able to completely download.
There is also a Garage Band library that you can delete if you're not using the Legacy sounds. The sample files are mostly AIF instead of CAF and take up a lot more hard drive space than the Logic Pro samples.
Don't empty your trash, incase you need to put back the items because you have problems downloading. You should only have the Audio Samples and plug in items in the trash if you emptied your trash before deleting the logic files.
Restart your mac. Launch Logic. It might state that it needs to download essential files so go ahead and do that. Also i find that plugging my laptop directly to my router does allow for faster downloads. Go to your Sound Library and select what you want to download. Hopefully you have enough disk space. If not you might need to empty your trash.
Also, just a tip. When you're in the finder. Go the View>Show Path Bar. This will bring up a bar at the bottom of your finder windows showing where you are in the finder. When you have that activate you can click on any prior folder to go back say two levels. In the pic you can could double click on Library to go up 3 levels. It makes it easier to get around.
Hope this helps

