Games : Minecraft crashing and corrupting world when exploring [on hold]

I'm having a problem with modded Minecraft. I haven't seen this problem before and have no idea what to do.

Every time I start my game and try to load more of the world, even parts of the world I have already been to, my game crashes and the world corrupts. I am playing on the FTB Infinity pack, newest 1.7.10 version.

Hardware specs:

16gb of ram (I have 6gb allocated to Minecraft, so it shouldn't be a memory issue)

Windows 7 64-bit

AMD A10-7850k APU with Radeon R7 Graphics @ 3.7 GHz

Full crash report: http://pastebin.com/77BEQtAu

This problem started after I ran a factory reset on my computer, because it had too much stored on it. My whole computer has been having issues since then, but I'm only worried about Minecraft. Everything was running fine before.

Any and all help would be greatly appreciated. One thing I haven't tried yet is reinstalling Java, so I'm about to try that. If it works, I will notify everyone.

Said it was unclear what i am asking, i am asking how to fix this problem how can i play my world without it crashing/corrupting everytime i walk like 100 blocks away from were i log on.