I am beginning to doubt that since it is a program installed on the PC, it would not be necessary to log in with an email and when losing the information on the hard drive, it would lose some vital .dat file in order to operate with that wallet.
Your assumption would be correct in the instance of Bitcoin Core. Bitcoin Core requires either a private key to be imported, or a valid wallet.dat file, and the corresponding password (if it was encrypted). Without any of these, you aren't going to get access to the wallet.