在开发个人电脑的过程中,他们克服了许多困难.
这样也许好理解一些：They overcame a lot of difficulties they had,developing the personal computer.
they had修饰difficulties,developing是现在分词结构作状语,表示...
完整的说法是They overcame a lot of difficulties when they were developing personal computer.
顺便说一句,difficulty应该用复数