Is it possible to do a cheap or free online or distance Ph.D. program?
To a first approximation, it's not possible.  There are few online or distance Ph.D. programs, and they usually have bad reputations.  A Ph.D. from a university with a bad reputation will actually be worse for your career than having no Ph.D. at all, so you should be very careful.  Plus these programs are as far as I know never free.  You can get financial support for Ph.D. work in several ways (competitive fellowships, a faculty member's research grant, teaching classes for the department), so depending on the field you may not need to pay anything yourself and may even earn a modest stipend, but that's not because the program itself is cheap or free.  Ph.D. supervision is intrinsically time-consuming and expensive.

I'm skeptical of how serious your question is.  Hoping for a free online Ph.D. isn't really reasonable; furthermore, if you have no time to attend a university, then you probably have no time to complete the years of full-time research required to write a Ph.D. dissertation.

However, I felt it was worth answering to warn you about scams from unaccredited universities.  There are plenty of diploma mills that will offer you a relatively cheap and easy Ph.D. online.  Such degrees are completely worthless, so they'd basically be stealing the fees from you.