The existence of non-physical minds (I'm looking for arguments other than the argument from the Hard Problem of Consciousness)

There's actually some medical evidence for this, but it's considered to be outweighed by evidence for mental materialism (eg lesions, Phineas Gage). There are case studies of people diagnosed with hydrocephalus as adults, who had something like 25% of the brain mass of the average adult, and yet this didn't seem to affect their mental abilities at all. I've heard of people citing this as evidence of mental tasks being performed by an invisible soul, not by neurons.

EDIT: (In case you want more info, here's the blog post where I heard about this. This is a personal blog I follow, but it links to some more official articles: http://www.rifters.com/crawl/?p=6116)