Hi Janej
If you have a property and an NIE number you do not need a padron and don't let anyone convince you that you do!! Padron's are for residents only in spain if you are not resident then you can't have a padron. I went through all this last year and I was being told by numberous people that you has to have a padron, not the case!!!
We bought a car privately and along with the seller all went to a Gestoria office in Mazarron I had to take a utility bill or deeds to prove I owned a property in Spain, my NIE certificate, passport and of course money!! The ladies in the notary office were fanastic, spoke English and they just did everything for you. The seller produced all the necessary vehicle documents which they then check to see there are no debts attached to the car then they send it all off for you to be registered in your name. There is a tax to pay and the amount depends on the value of the car you are buying. All you do then is go back to collect your paperwork when it comes back from the police.
I was really apprehensive about the procedure as everyone was giving me conflicting information but it was easy peasy in the end.
The Gestoria/notary office was right at the back of the little park/foutain area in the centre of Mazarron