Was Luther's belief that the church's foundation was faulty to begin with, or that through time it fell into an apostate state and needed to be reformed back?
Luther, like other reformers, regarded the early church highly, but not above scripture. We see this in two ways – (1) he accepted the earliest councils of the church as faithfully proclaiming the truth of scripture and (2) he respected many of the church fathers and benefited from their insights, though always judging them against scripture.
Manfred Schulze, in his article "Martin Luther and the Church Fathers," in The Reception of the Church Fathers in the West, I, helpfully reviews Luther's interaction with the fathers. But he also describes Luther's acceptance of the first four ecumenical councils:
The four "principal Councils" of Nicaea, Constantinople, Ephesus and Chalcedon were (for Luther) all distinguished by the fact that they did not resolve on any new articles of faith, till then unheard-of, but provided genuine instruction from Scripture. [...] The doctrinal pronouncements of the four principal Councils are really "Holy Scripture" for Luther, because they derived from genuine exegesis of Scripture by the Fathers of Councils. (590)
So it's clear then that Luther felt that in the essentials, the early church got off to a good start, since it faithfully taught the Bible in its first four Councils.
Luther's respect for the church fathers is also clear, but again he places them under the authority of scripture. Brian Litfin writes:
Martin Luther warmly embraced the church fathers whenever their comments dovetailed with scripture. Luther's biblical commentaries are full of patristic citations. He tells us he had thoroughly studied the fathers, and even endorsed the ideal of a reformation based upon their writings and the ancient creeds. (Getting to Know the Church Fathers, 27)
That said, Litfin makes Luther's selectivity clear in a footnote:
Luther's approach to the church fathers was always selective. When he found them to be in harmony with scripture, he accepted them. When he believed them to be contrary to scripture, he felt the freedom to reject them on that point. (270)
One way Luther compared the relative authority of the Bible and the fathers is by adopting the analogy of St. Bernard, in On the Councils and the Church (1539):
He [St. Bernard] admits that he held the holy fathers in high esteem, but was not by any means an entire convert to their opinions. He assigns the following cause, and draws this comparison, viz., that he would prefer to drink from the fountain at once than from the streamlet. [...] Thus must the Scriptures hold the rank of master and judge, otherwise should we have too much recourse to the brooks [the church fathers]. (22–23)
Based on all this, we'd expect that Luther appreciated some fathers more than others. And that is indeed the case. Perhaps foremost among them was Augustine, who paved the way for Luther's views on sin, but (according to Luther) still didn't fully understand Paul. Luther also thought that even the doctrine of justification by faith alone could be found in several fathers, though he wished it appeared more clearly. Manfred Schulze writes:
At the beginning of his great lecture on Genesis Luther reports that because he knew of justification by faith from Scripture he also found it in Augustine, Hilary, Cyril and Ambrose, even if they did not zealously pursue it in practice and at time talked about it only inappropriately. "But I don't count that as an error on their part" is his conciliatory comment; "it suffices if they say the same thing on the subject; even if they scarcely express it appropriately, their testimony bears me out". (612)
Schulze's article mentions other fathers toward whom Luther was less generous, like Pope Gregory, who "produced nothing good with his teaching" (612), Jerome "does not know what the gospel is and does not understand what the law amounts to" (609), and Origen and Cyprian, neither of whom "preached Christ" (615). Schulze concludes that the fathers were merely "theological controversialists" for Luther, "no less, but also no more":
Church Fathers are criticized, but are also praised for having assembled much that was correct, e.g. on the Psalter, even if at times their expositions of the meaning of the text diverge widely. The same as happens to all exegetes is the fate of the Fathers too in their exposition of Scripture—"One makes a mistake here, another there." (615)
Luther certainly believed that there was much of value in the early church – the first four councils, and many of the writings of the fathers. So it is fair to say that he saw his work as a reform, and not a completely new beginning. But at the same time, he did not regard those in the early church as authoritative – ultimately he judged everything against the singular authority of the Bible.
Martin Luther wanted the Catholic Church to reform itself and return and refocus on the Bible and less on the words of the priests and pope, which he believed to have strayed from the original teachings. Most of the issues he dealt with in the 95 theses were very new, or only surfaced in the last few hundred years of the Catholic Church, so I'd say it's safe to say he had no problem with the early church, just the bureaucracy he perceived in the Catholic Church at the time.
Sources: Luther's Small Catechism, Lutheran Confirmation, and http://www.greatsite.com/timeline-english-bible-history/martin-luther.html