What version of Premiere Elements and on what computer operating system is it running - from the sounds of it, you are using Premiere Elements 10 and earlier. There is no longer a "Sign In" for Premiere Elements 10 and earlier once photoshop.com was discontinued. This is an old story.
The answer is to ignore or cancel out of the photoshop.com messages and continue into the program for import, editing, and export.
Also, you may see photoshop.com plus members only content. Although you see the thumbnails, the content is not available to you.
Was the install of the program with your purchased serial number successful?
Please let me know if you need further information on the above.