Submitting more accurate answers and using a known computer/IP-address will help.
The only account recovery option Google provides starts at (an account can not be recovered by posting here or contacting Google). Lacking backup codes, the only option is to use the account recovery form (verify your identity) to try and regain access to the account. Even a backup phone number would have fixed this (it could have been a voice/land-line). Those codes are for exactly this sort of situation and would have you back into the account in seconds ( ).
This is where you use one of the backup codes you were instructed to save when you enabled 2-step verification on the account.
