My two cents:

It seems like in this situation you should not have to pay.  3 1/2 days for an update is ridiculous.  What is this persons stated turn-around times?  I always give my clients my turn-around times.  If I dont meet those and dont make any attempt to contact the client to give them an explanation, then I am not entitled to payment because I would not have lived up to my obligations.  I dont give out my cell # to clients anymore because I got tired of getting status calls every 15 minutes, but my clients can always leave a message via my office phone, fax or e-mail.  I wont put up with the people that want to call for status every 15 minutes and interrupt me from actually doing the work, but I always maintain numerous was to keep the lines of communication open.  I dont respond to status calls within the first 24 hours, but if it is going to take longer than that, I let the client know.  There is a certain balance that has to be reached between the client and vendor.  These policies seem to have worked for me so far.  Many clients will simply hound their vendors to death.  I have had orders come in after 5pm one day (so there is no way I can work on it that day) and had 7 status calls on that order before noon the next day!  Are you kidding me?  In this situation however, you gave them two days before you cancelled and it was still a day and a half later before they sent the work in.  How can they reasonably expect to get paid for that poor service?  The only exception to that would be if it was actually within their turn-times.  If for instances, that was in a county that they have told you would take four days, then technically they would be within the service window promised.  In this case, I still dont think they should get full payment because they didnt keep the lines of communication open.  You did get a fax to them cancelling the order after 2 days and it was another day and a half before they sent the search in.  As far as not having their phone #-- have they moved their office recently?  When I moved mine it took numerous attempts to get things right with some clients.  First I sent a fax with all my new information and called all of my clients personally to make sure they had the new information.  I was personally told by all clients that they had the new info.  Then there were a few clients I didnt get any work from for a while.  I called them and sure enough, they looked in their system and they had the old info in there.  A couple of  them it even took another call to get it right.  One client I called three times and all three times they still had the old info.  All three times they told me they changed it in their system, but the next time I would call it was back to the old info.  I finally gave up.  I have still not received another order from them.  Another client took three calls to get my mailing address right.  They got the phone/fax info right so they could send me orders, but didnt seem to care about getting my mailing address right so I could get paid.  I'm not saying this is what happened in your situation, but sometimes these things do happen.  It certainly seems in this situation that it is just an irresponsible vendor.