Blinking question mark on folder on boot

If only the arrow comes up when you hold down option it most likely means there's some kind of hardware issue. You may be able to repair it using the Disk Utility in Internet Recovery (Hold down ⌘ command+⌥ option/⌥ option+R while booting) , but I'd advise in to looking to getting this thing serviced or repaired. Sounds like you've got a bad HD.

If all else fails, run fsck and see what happens. Information on how to do that is located also in the provided article.

Here are your Options.

We assume your Boot sector is somehow damaged.

We further assume your hard drive is not damaged.

Since you installed Mountain Lion you might be in luck.

When you install Mountain Lion or Lion, the installer creates an invisible, bootable, 650MB partition—a portion of a drive the operating system treats as a separate volume—on your startup drive called Recovery HD that includes a few essential utilities for fixing problems, restoring files, browsing the Web, and even reinstalling the operating system.

The installation is not always given factor so it might not work for your system.

Easy to find out by Restart while holding the CMD - R.

If you have a Recovery on you drive it will come in to action, then follow the steps.

Option 2:

If you do not have the Recovery installed or your disk is damaged, the Try with Target disk mode.

For that you will need a second Mac.

If you have access to a working Mac, and both it and the non-working Mac have FireWire or Thunderbolt ports, boot the non-working Mac in target disk mode by holding down the key combination command-T at the startup chime.

Connect the two Macs with a FireWire or Thunderbolt cable.

The internal drive of the machine running in target mode will mount as an external drive on the other machine. Copy the data to another drive.

Others:

Here are all Start up keyboard combinations you can try.