I had this problem myself and investigated it for some time. At the end I narrowed it down to browser cookies. I was using browser add-on to clean the cookies after a site session is closed, and it apparently killed both the PayPal cookies and cookies which were used by the website where I initiated the PayPal transaction and which obviously were needed to complete the transaction. So if your cookies are disabled in your browser settings, or you installed a cookie management add-on that cleans the cookies on-the-fly, and if your merchant relies on cookies to complete payment process, you are likely to have this problem. Once I whitelisted merchant and paypal web sites in my cookie add-on, the problem disappeared and I was able to successfully complete the transaction. The "Want to complete your Paypal Payment" email seems to come from the fact that you probably tried to refresh the browser page where the transaction was stuck, and it somehow initiated duplicated transaction attempt, which was then detected by PayPal and it sent a misleading email about it.
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