I figured it out!

I had to go to Configuration in my Joomla backend for JoomSEF. In there I filled in the JoomSEF Download ID with the ID sent in the email after purchase.

Then I went to Upgrade, again in Joomla's JoomSEF backend, and clicked on 'Reinstall from ARTIO server.'

Voila!

I just purchase JoomSEF 4.0. I had the free version of joomsef 4.4.3 installed in joomla 3.1.5. I clicked on the download link in the email I was sent, entered the Download ID, and downloaded JoomSEF 4.0. I then went to JoomSEF update in Joomla backend, chose the com_joomsef4.zip file that I downloaded from the link received after paying for the component, clicked on upload & install, and got the following error messages.

'ERROR: Download ID not set'
'WARNING: Component Install: Custom install routine failure'
'MESSAGE: Error installing component'

Can you tell me what I'm doing wrong? Is there somewhere I'm supposed to 'set the download ID?' I did enter the ID code on the website to download the component.

Thanks for your help.