Snow Leopard did not have a Recovery Mode. Recovery Mode only first appeared in OS X Lion and Internet Recovery even later. For Snow Leopard you would need the install disks to erase the internal drive.
Without the install disks, do the following:
- Remove all personal data files - move to Trash then empty Trash.
- Sign out of iTunes & iCloud
- Uninstall all apps other than the ones that came with OS X
- Reset NVRAM
- Log into your Admin account. Create a second Admin account with a generic password. Log out, then log into the new Admin account. Remove the old (existing) Admin account.
