Is there anyway to definitively know if your SATA cable is dead on a macbook pro?

Maybe I need to plug the laptop into the power before it cuts out.

There is NO maybe about that, thats horrible on your battery, it will destroy it FAST if you continue to do that.

SATA cable is $15 last I looked, so your $60 figure is incorrect.

Without hands on diagnostics, your SATA cable indeterminate, however from your indicated chain of causation, Id dare say its unlikely your SATA cable.

A flashing question mark appears when you start your Mac

At worat you may need to reinstall OS X:

Reinstall Lion, Mountain Lion, or Mavericks without erasing drive

Boot to the Recovery HD:

Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.

Repair

When the recovery menu appears select Disk Utility. 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 then click on the Repair Permissions button. When the process is completed, then quit DU and return to the main menu. Select Restart from the Apple menu.

Reinstall Mountain Lion or Mavericks

OS X Mavericks- Reinstall OS X

OS X Mountain Lion- Reinstall OS X

Note: You will need an active Internet connection. I suggest using Ethernet

if possible because it is three times faster than wireless.

I think the only way to know is:

1. Be sure the SSD model will work with your computer model.
2. Check your installation to be sure the cable is properly aligned with the pins, properly seated, and connected to both the drive and the motherboard. If it still doesn't work then find a new cable to replace it.

Have you tried the cable with the original drive? Does that work? If it does then there's nothing wrong with cable.

Given the model you have it only supports SATA i and SATA II drives. Try getting a drive that definitively supports SATA II. Preferably, don't use SATA III drives because some may not work.

A good source for SSDs that will work is OWC. Their Mercury 3G drives should work just fine.