Urgent: Registration Flow Not Working Due To Automatic Login Not Working

Hi, I'm desperately trying to fix this:

On my site, the registration flow was working before. But recently, the automatic login after registration doesn't work anymore - which means users are then forwarded again to the registration page instead of being forwarded to the payment page.

I found this problem referenced in another thread which hinted the problem could be w3 total cache - I've uninstalled this completely using the references in this thread. But the problem is still there.

We've got a promotion coming up in a couple of hours - if I cannot get this fixed I will lose money.