Check the file share that was set up where you are trying to backup/restore from. Right click on the directory and select Properties. Select the "Sharing" tab, and then click on the "Share..." button in the Network File and Folder Sharing section. Look at the list of users allowed to access the directory. I would expect that you will see the login for the service account for the server where backup/restore works correctly, but do not have the service account used for the server where you are having problems. Click on the the drop down list and select "Find people...", then enter the account for the server where you are having access problems. By default it will add the account with "Read" permissions only - you will have to click on this and change it to read/write if you need to perform backups as well as restores.