The Padma Purana is one of the eighteen Mahapuranas (Major Puranas), and it includes many important things, including a retelling of the Ramayana, a religious dialogue between Shiva and Parvati called the Shiva Gita, and several Sahasranamams (lists of 1000 names of a god), including a Vishnu Sahasranam (different from the more famous one that Bhishma told in the Mahabharata), a Rama Sahasranamam, and a Venkatesha Sahasranam (in praise of Venkateshwara).
As far as I know, the only unabridged English translation of the Padma Purana is this 10-volume translation by N.A. Deshpande from the 1950's, published by Motilal Banarsidass. My question is, is the whole translation available for free on the internet? I've found most of the volumes of it online, as I discuss in my answer, but the whole thing still eludes me.
Naturally, since this is a reputable site, I only want legal sources, nothing that involves any copyright-infringement.