SQL Server – Restricted User on Local Database

You've explained that you don't have the SA password and you're not an administrator. In that case, you're going to have to hack your way around it.

See Think Your Windows Administrators Don’t Have Access to SQL Server 2008 by Default? Think Again. by Argenis Fernandez.

That post explains how to impersonate the NT AUTHORITY\SYSTEM login using PsExec (or creating a Windows Scheduled Task running under the SYSTEM account) to create a new login for yourself. Then, you can log in via that new login, and grant your Windows account SA permissions.

Well, suppose you have a command to execute your backup like this

BACKUP DATABASE [naass] 
TO  DISK = N'C:\program files (x86)\Microsoft SQL Server\MSSQL.3\MSSQL\Backup\Naass.bak'' 
WITH NOFORMAT, INIT,  
NAME = N'naas-Complete Database Backup', 
SKIP, NOREWIND, NOUNLOAD,  STATS = 10

this will fail if the process that executes this command doesn't have the permissions to write in the mentioned folder. And Windows 7 (for very good security reasons) keeps the C:\program files folders and its subfolders write locked also to an administrator account.

You could mess with the default permissions and give to your folder above write permissions for your account but of course this is not the recommended way.
Much better, simply change the script to work on a different directory on your disks.

BACKUP DATABASE [naass] 
TO  DISK = N'D:\BackupSQL\naass.bak' 
WITH NOFORMAT, INIT,  
NAME = N'naas-Complete Database Backup'
SKIP, NOREWIND, NOUNLOAD,  STATS = 10

Of course this new directory should have the correct permissions.