How comfortable are you regarding opening your mbp, putting in a new hard drive or SSD, and using the terminal app? And what year is your Mac? Do you have other computers available that you could possibly use to query and inspect your old hard drive?
As a first step, I advise removing your old hard drive, put it in a safe place for a while, put a new (blank) hard drive or preferably a SSD in your Mac, then restoring your original OS, then running hardware diagnostics extensive mode and multiple times. Optionally after that, you can upgrade to El Capitan, and then run diagnostics again and again. After that, what to do depends on what computers you have available and your comfort level with apps like terminal.
(I had some more detail advice and had almost finished typing it all when I connected a good drive via a NEW USB enclosure to my computer JUST to find out OSX naming scheme in regard to discs ( /dev/diskN where N=0,1,2,3,…) and a few minutes later my mac book air kernel panicked and gave me a grey screen. Probably the enclosure wasn't developed and tested with OSX. If my reply was autosaved I can't find it... )
One of the first things you may want to do, even if you send the drive off to an "expert", buy another external hard drive of equal or greater size than you old drive and then in terminal do something like (I welcome discussion here!):
dd if=/dev/disk1 of=/dev/disk2 bs=4096 conv=sync,noerror
http://serverfault.com/questions/4906/using-dd-for-disk-cloning
Along with the programs Niel has mentioned, there is freeware out there, see
http://askubuntu.com/questions/211578/whats-the-difference-between-ddrescue-gddr escue-and-dd-rescue?rq=1
