What account is your SQL server running as? Network Service? Local System? Domain account?

If possible, change the service account to a domain account as thats best practise solution, and then assign that account read permissions to the drive in question. Also your using G$ which is an admin share, so the account will need administrator rights. To get around this, create the Data folder as a share and grant permissions on the share to prevent giving admin rights where they are not nessesary.