The distinction between poetry and prose has never worried me too much. The only people who need to worry are judges, editors and anthologists - if they get it "wrong" they'll receive lots of feedback and might not be asked to do the job again. Some people try to define poetry based on analysis of the text, often using unquantifiable terms like "density" and "intensity". Sound is frequently mentioned in these definitions. This approach faces several problems
Reader-centred approaches seem more useful. Rather than classifying texts as "poetry" or "prose", there are "poetic" and "prosaic" ways of reading. Some texts reward a poetic reading more than they do a prosaic reading. Readers have expectations when told that a text is a poem, and their reading strategy is different for poetry than for prose. There'll be variation between readers, and some readers may change their reading strategy according to the poem's sub-genre. Here's a list of some common expectations and assumptions based on P.Begemann's "Reader's Strategies in Comprehending Poetic Discourse"
Some of these expectations are shared by viewers of art works in general. None of them is essential.
Some people adopt these strategies readily and in many contexts. More often, something needs to trigger such a response. Most poems are clearly signposted as such (e.g. they're in a poetry book, or they have line-breaks) so readers generally know when a poetic strategy is being suggested.
A found poem is a piece of text whose context is changed so that readers are encouraged to adopt poetic reading strategies. When Yeats added some of Pater's prose to a poetry anthology he needn't have added a title and line-breaks, but doing so reduced the chance of rejection by readers.
I don't think that the above description should be controversial - to me it merely describes how readers behave. Readers of maths texts, detective novels, recipes, etc will also have expectations and strategies. They too will need to contribute to the text, but they'll be faced with fewer borderline cases (in particular, they'll be faced with few works that deliberately challenge the borderlines). Reader-centredness raises some issues for the writer
To increase the poetic effect of a text, poets can make the text more "poetic", or they can make the reader adopt a more poetic approach. Context and the author's name are important factors in the reader's choice of strategy, and shouldn't be disregarded by the writer. It's not so much that rhyme and line-breaks (etc) identify a text as a poem, but that making a piece of text look like a poem encourages readers to treat it like a poem.
For poetry to exist, there needs to be a text, a reader, and a suitable "poetic" reading-strategy/setting. In Acumen 54 (Jan 2006) Judy Gahagan wrote "the once unique poetry habitat is a threatened one", a metaphor which can be extended. When a species' habitat shrinks, a few things are likely to happen