So you have moved your WordPress site to another ISP / Hosting provider and changed the url or name of the blog.
Whenever you do a manual upload of an image or plugin etc you get a message similar to:-
Unable to create directory /wp-content/uploads/ Is its parent directory writable by the server?
For this example I am going to call my old blog – adigraham1 and my new blog adigraham2
1. Login to your blog as admin, go to Settings, Media (WordPress v3.8) and look at the directory path in Store uploads in this folder path
2. In that path you will have the old site name e.g /home/adigraham1/public_html/wp-content/uploads/year/day
3. Change the name of the old site to the new site e.g /home/adigraham2/public_html/wp-content/uploads/year/day
4. Save and try uploading a file again