Registration is understood as registration at the place of residence with a corresponding note in the passport confirming this fact. The lack of confirmation of registration entails a lot of problems. So, you may have difficulties in obtaining a compulsory health insurance policy, when visiting a medical institution, placing a child in a kindergarten, you are not recognized as needing to improve living conditions, and so on.
To restore your rights and confirm the fact of permanent residence at a specific address, you must contact the courts. But first, you should send an application to the service that said “no” in response to your oral appeal (passport office, insurance company, Pension Fund Office, etc.), attaching documents confirming your actual residence at this address. This can be an order, a certificate from the house management, a receipt for payment for housing and communal services, a pension certificate and other documents that indicate your place of residence. Since these papers are not indicated in the relevant laws and instructions (it is the registration stamp that is required), you will most likely receive a written refusal to satisfy your request due to the lack of registration. This will be enough to apply to the courts with a statement to establish the fact of permanent residence. Together with him, the above written refusal, your passport and the same documents confirming actual residence (copies are possible), as well as a receipt for payment of the state duty are provided. If this is not enough, then you will need people (friends, acquaintances, neighbors) who can confirm that you really live at this address. This means that you will have to write an appropriate petition to summon them to court as witnesses. As soon as this fact is established (and you will have to be patient, because the proceedings can last more than one month), you will need to submit the appropriate court decision to the service that refused your request and demand its implementation.