Consulting Rates?

After applying and interviewing for a Marketing Director position at a
small high-tech company, I was told they've decided not to fund a
full-time position now but may wish me to work with them as a
consultant on specific projects. I'm open to such an arrangement, but
having never consulted in this field I'd like some feedback on what
rates might be considered standard and/or reasonable under the
circumstances.

For the sake of argument, let's say that the full-time position would
have paid $80,000. That would be $40/hour based on a standard working
year. Add the benefits that a self employed person must provide for
him/herself plus the other costs of part-time self employment, and it
seems to me that twice that, $80/hour, could easily be justified. On
the other hand, I know that the company views this in part as a kind
of internship in their industry, with which I am not familiar. And
they're trying to save money with the consulting arrangement. I
suppose another potential complication might be the idea of
per-project fees rather than hourly.

Add this all up and I'm uncertain what to ask for or agree to. Any
thoughts would be appreciated. Thanks.