Desktop Publishing Issue - Sign On

Hi Mk2018, 

The account mentioned in "You don't seem to have an account for Power BI. Please click the button to sign up" is Power BI service account, rather than computer account. 

When you click on Publish button in Power BI desktop, it requires us sign in Power BI service account. For detail information, you can see: https://docs.microsoft.com/en-us/power-bi/desktop-upload-desktop-files

In your scenario, it looks like you don't have a Power BI service account. If yes, please sign up a Power BI service account firstly follow this document: https://docs.microsoft.com/en-us/power-bi/service-self-service-signup-for-power-bi

Best Regards,

Qiuyun Yu