Access Denied error in CREATE DATABASE ... FOR ATTACH
When you get this message it can be a few things. Some examples:

1.) Read Only Marked Files

2.) Insufficient permissions to the files for the SQL Server Service account

3.) Insufficient permissions to the folders the files live on. 

You indicated in our chat that this was not read only. You also verified permissions looked like full access. That ruled out these three items.

The fact that, from our chat conversation, you were not experiencing this issue when you properly detach a database using sp_detach_db - which actually changes permissions around a bit on the files led me to suggest trying to run SSMS as administrator.

Why? Well this article gets into a lot more nitty gritty about some of the impersonation issues here - but my understanding is:

1.) When you just stop the SQL Server Service and move the file around. The owner of the file is the service account that created it.

2.) When you detach the database - you'll potentially notice a permissions change. The owner has changed basically and the file is not really associated with that SQL Server service account the same way.

3.) So it works when you try to attach because the permissions can get assigned, because the security of the file allows it..

But if you just stop the service the security hasn't changed, and you can't attach that if you have UAC enabled unless you are impersonating administrative access. 

I've probably made the file ownership and access more confusing here but the article I shared probably does a better job :-)

But one slight moral is - do a detach next time ;-) Or just be prepared to run SSMS as administrator from time to time when interacting with the OS in various ways.