Sub clause is in past perfect tense and main clause must bring the sentence to present perfect and then make a future prediction.
A] has not and possibly never will be able to run [Incorrect present perfect – eliminate it
B] has not and possibly will never be able to run [Incorrect present perfect – eliminate it
C] has not been and possibly never would be able to run [Hold it
D] has not and possibly never would be able to run [Incorrect present perfect – eliminate it
E] has not been able to run and possibly never will be able to run [Ok – Hold it
]Struck Between C and E:
Both will and would are virtually interchangeable, but the major difference is “would” in main clause can express a hypothetical meaning.
Since C has already expressed “possibly” – an hypothetical, then E is the best option.
Please refer following site for more information:
Uses of Will and Would http://grammar.ccc.commnet.edu/grammar/auxiliary.htm#would
In certain contexts, will and would are virtually interchangeable, but there are differences. Notice that the contracted form 'll is very frequently used for will.
Will can be used to express willingness:
I'll wash the dishes if you dry.
We're going to the movies. Will you join us?
It can also express intention (especially in the first person):
I'll do my exercises later on.
specific: The meeting will be over soon.
timeless: Humidity will ruin my hairdo.
habitual: The river will overflow its banks every spring.
Would can also be used to express willingness:
Would you please take off your hat?
It can also express insistence (rather rare, and with a strong stress on the word "would"):
Now you've ruined everything. You would act that way.
and characteristic activity:
customary: After work, he would walk to his home in West Hartford.
typical (casual): She would cause the whole family to be late, every time.
In a main clause, would can express a hypothetical meaning:
My cocker spaniel would weigh a ton if I let her eat what she wants.
Finally, would can express a sense of probability:
I hear a whistle. That would be the five o'clock train.