Website for appointment for NIE Renewal

If you cannot follow the advice as the system is not working.  In your situation I would go to the police station, explain the problem and ask for an appointment.   If they do not oblige demand the complaints form

In similar situations I have done just that and everything was resolved immediately and the police apologised

I may have found the answer

If you ignore the warning I believe you can go to the page you need

I have found on several occasions Spanish government web page show the same warning but having ignored and accepted I have achieved my object and have not suffered any adverse problems

Hi John,

Thank you for the reply.  I took my laptop and mobile back to the police station to show them (along with printed screen shots) and this is what we discovered.  The site is not accessible form Apple products.  The warning page on Apple products does not allow you to go past the page and enter the site.  If you click on Proceed to site (unsafe), you get an error message. 
One of the police officers even had me download the browser "Opera", which is what he uses on his Samsung phone.  When he tried the site from Chrome it didn't work, but it worked from Opera.  So, when I had Opera installed, we sat side by side and typed the same information in the browser and his device opened the site, where mine said "cannot open site". 
Both my husband and I have Macbook Airs and iPhones, so even though he was in Algeria (I had him try the URL), neither of us could open the page.
This also explains why I was previously having problems with the foreigner's office, because I could not access the instructions or download and print form 790...and nobody believed me.  Apple does not allow access to the site based on the coding and the site is not secure....apparently.  Now I know.  If anyone else is having problems with the government sites and accessing forms, switch to Android.
Oh, and they made the appointment for me upon discovering I was telling the truth

When I checked and encountered the warnings i was using my Apple iPhone 7.  So strange

Glad to hear you now have the appointment

Ah, you're right, You can move past the warning on iPhone...however, it did not work on my Air. 

In Firefox, I get this message, which takes me to the HTML code:
sede.administracionespublicas.gob.es uses an invalid security certificate. The certificate is not trusted because it was signed using a signature algorithm that was disabled because that algorithm is not secure. Error code: SEC_ERROR_CERT_SIGNATURE_ALGORITHM_DISABLED

In Chrome, the link is broken to bypass the warning. In Safari, I am asked to change my certificate trust codes.

Now I know I can use my phone for this.  Thank you.