Hi Tina
You still get your NIE at the police station, have you booked an appointment for this, some stations in Alicante are by appointment only as they are now very busy, i believe you can still go to Elche and get same day by queuing, however if not all you do is go in and book a future day/time. The stations used to give you the 3 carbon copy 790 form but they no longer supply them, if you click the link below it will take you to a web site so you can download it. If you have access to a photocopy (Kodak stores do a copy for appx 20 cent) fill in the master and take 2 copies, otherwise print out 3 copies and fill them in, take to any bank and they process and stamp each form, they keep one themselves, one is your copy and the master for the police. You pay the bank approx 9.45 euro for non resident NIE and full resident NIE is just over 10 euro.
Once got 790 stamped take with all other documents to the station, please ensure you have photocopies of everything you need as the police cannot copy anything for you.
Another station where you can queue for same day without any appointments is in Valencia region, gandia station, opens at 9am week days.
Hope this helps
Anna