How much free space do you have on your HDD?
Plenty of space 1.63TB
Premier Elements installs without issue on a lot of machines, including mine. Something is unique with yours.
You have the option of listing the full details on this user forum and some will do their best to help. So far you've said you have Windows 10, lots of hard disk space and version 15. That is not enough for any in the user category to begin guessing with solutions, let alone answering your particular issue.
I suggest you contact Customer Support. Google for "adobe customer service". You should get a phone number and links. I've never had to use them, but reports are that they can go so far as to remotely run your machine and find the problems.
Good luck. It is never fun when something that normally works for everyone else does not work for us!
After more research, I found the problem with the software not opening. Lavasoft Web Companion was the problem. I uninstalled it and both photoshop and premiere will open.