I have a basement wall that has begun falling apart on the inside of the wall. I have begun to dig on the outside to waterproof and seal the wall at the foundation. Once this is completed what is the best course of action to start repairing the inside where it has started to crumble?

Well, a good mason can chip out the old damaged blocks, and install new ones, one, or even a few, at a time. A block wall will naturally "arch" over an opening cut in it, if the opening is cut with care. I suggest you do this, or have it done, before you do anything outside. Don't worry, if blocks are removed by someone who knws what he's doing, the basement wall will neither collapse nor crack.

And congratulations for offering proof that water, when allowed to run freely through a block wall,. can absolutely deteriorate some blocks. I have a client who can reach down and remove parts of his bottom course of block WITH HIS BARE HANDS!! Water is both the most beneficial and the most destructive force on Earth. We can't live without it, but we must try to tame it where need be.