Macbook Pro can only startup with external hard drive connected Here are the facts:

13 inch, mid 2012

It gave me the grey screen with the flashing question mark folder one day, and I got an external hard to install the MAC OS X operating system like the apple support pages said.

My MacBook Pro now works....until I take out the external hard drive, then it's back to square one with the same problem. I determined that in Disk Utility, the external hard drive I used to reinstall Mac OS X is being used AS the startup disk needed to get my computer working. My MacBook no longer has an INTERNAL hard drive listed, and it is not the kind where the battery can be removed from the back. I need to know if there is any way to make one before I take it to the shop.
If disk utility does not show your internal disk anymore it is a Hardware, not a Software fault. Unless you are savvy enough to troubleshoot the hardware issue yourself you will have to take it to a repair center. 

Most likely it is actually not the Hard Drive but the Hard Drive cable that is failing. It is a common issue with your model and you might be eligible for a free replacement (cable). Be sure to either contact Apple Care or go to an Authorized Repair Center and have them check the issue for you.