@Apollogrottos,
Hello,
This is how I would parse it:
1. The simple subject is "part."
2. The linking verb is "is."
3. The predicate noun is the noun clause (introduced by "that") : "Meno himself has too much culture."
*****
"Of the problem" is a prepositional phrase that modifies "part."
"in Plato's Meno" is a prepositional phrase that modifies "problem."
James
P.S. That Meno himself has too much culture is NOT the problem. That is only PART of the problem.