NIE numbers and certificates are issued by the National Police departments in Spain. You will not see a policeman but a chap in a suit who is responsible for keeping the records.
Only the National (as opposed to local or Guardia Civil) police can issue a number. Even if you go to a foreigners office (like one in Torrevieja or Orihuela Costa) then they will have access to the National Police computer system to issue the number. The same as the consulates in UK who also have access to the same database.
Now, there is a National Police station in Elche, Orihuela and Alicante in this area plus the foreigners office in Torrevieja and Orihuhela Costa.
You need to make an appointment online before turning up.
You can do that online at this website
Cita Previa(You can use Google translate to walk you through it).
If Euromarina did it for you in the first place (and I would suggest it was their solicitors with a power of attorney) then you should ask them where they got it from and arrange an appointment there.
The National Police offices in Spain are responsible for issuing NIE numbers and certificates and residency certificates.
You need to fill in a EX15 form (the same as would have happened for the original but you can get a solicitor or agency to do it for you for a cost) and the payment form which is a modelo 790.
You can download that form at this website
Fee For Foreigners Payment and that generates a Modelo 790 tasa 052 (which is if you do it at a foreigners office)
If you are going to a National Police station then you need the Modelo 790 tasa 012 which you can download from this website
Model 790/012.
Once you have made your appointment online and downloaded the correct payment form, take the Modelo 790 to a bank and pay the fee and then the receipt with you for your appointment including the EX15 and passport.
Hope it goes OK. A solicitor/agent will probably charge you about 70 euro for doing it.