OSX won't see hard drive...

If the drive fails to appear in Disk Utility then it is most likely dead.

Most likely because there are no permissions to repair. It's a backup drive with no bootable system. You can only repair permissions on a bootable disk and, then, only system file permissions.

What you need to try is to repair the drive:

Repair the Hard Drive

Open Disk Utility in the Utilities folder. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the installer.

If DU reports errors it cannot fix, then you will need Disk Warrior and/or Tech Tool Pro to repair the drive. If you don't have either of them or if neither of them can fix the drive, then you will need to reformat the drive and reinstall OS X.

This isn't a Time Capsule is it? If not try this way:

Boot from your Installer disc. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Utilities menu. After DU loads select the external volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the installer.

If DU reports errors it cannot fix, then you will need Disk Warrior and/or Tech Tool Pro to repair the drive. If you don't have either of them or if neither of them can fix the drive, then you will need to reformat the drive and reinstall OS X.

So, then, Disk Utility can't repair the drive. What errors did DU report? You may need to try

Disk Warrior to repair the drive if it's reparable. If not then you will probably have to reformat the drive. In that case you may need to recover data that's recoverable. See the following:

Basics of File Recovery

General File Recovery

If you stop using the drive it's possible to recover deleted files that have not been overwritten by using recovery software such as Data Rescue II, File Salvage or TechTool Pro. Each of the preceding come on bootable CDs to enable usage without risk of writing more data to the hard drive. Two free alternatives are Disk Drill and TestDisk. Look for them and demos at MacUpdate or CNET Downloads.

The longer the hard drive remains in use and data are written to it, the greater the risk your deleted files will be overwritten.

Also visit The XLab FAQs and read the FAQ on Data Recovery.