Were the Brazilian elections of 2014 democratically legitimate or was there fraud?

Fraud.

1. Smartmatic, the company that provided the software, is a Venezuelan company created solely to perpetuate in power members of the Foro de São Paulo through election fraud. This is a widely known fact, any google search of the terms "smartmatic" and "fraud" will reveal hundreds of sources.
1. merely letting any Smartmatic-associated personnel near any part of any election process is grounds for nullification of the election. Any country that calls itself "democratic" is bound to treat Smartmatic as an hostile actor, much like an enemy spy - they are no different from that.
2. Contracting with Smartmatic to supply even a power cable is election fraud by design. And they supplied all the software in 2014.
2. Diebold, the company that provided exclusively first-generation, non-auditable, hardware that does not afford even the basic security was found in the US to having had engaged in "a worldwide pattern of criminal conduct", according to US Attorney. Again, 5 minutes with Mr. Google will land you hundreds of clear-cut cases of fraud.
1. While many sound competitors abound, the only purpose anyone would single out Diebold as a hardware supplier is to perpetrate fraud.
3. The vote counting was secret, which is fraud by design.
4. In 2008 unknown hackers effectively defrauded the election system and auctioned off votes. Authorities declined to comment. No action was taken whatsoever.
5. In 2012 an unnamed hacker, known only as "Rangel" effectively defrauded the system, auctioned off votes to the highest bidder and later testified to this fact. No action was taken whatsoever.
6. The election of 2014 was presided by Mr. Toffoli, who was the incumbent's attorney the election before. Highly suspicious, but not fraud per se.
1. Mr. Toffoli effectively prohibited any serious attempts by internationally renowned information security researchers (hackers) to audit the software or hardware before the election by introducing strict timetables, incomplete access etc. such prohibition is fraud by design.
1. Even with only limited disclosure, many flaws were found but were totally ignored by officials. No actions were taken.
7. Election day. Several cases of fraud were caught in tape in broad daylight. By law, the election should have been nullified. No action was taken.
8. As 76% of Brazilians don't trust the voting machines (old data, must be around 90% now), a public uproar for a post-election recount pressured the losing party to ask for it and they reluctantly complied.
1. Their extensive "audit" concluded only that auditing was impossible.
9. In march 21, 2015 The Washington Conclave for Democracy, attended by personalities such as Jeb Bush and Senator Marco Rubio, presented a detailed benford-newcomb analysis with publicly available data - completely reproducible by anyone with basic numeracy skills and an spreadsheet.
1. The conclusion was very clear: Dilma did not receive a majority of votes.
2. While fraud was known to happen before in municipal or state level, this is the first time a President clearly defrauded a nationwide election.

A wealth of information and further discussion can also be seen here.

As a personal anecdote: municipal election of 2008, the candidate I voted for alderman registered precisely zero votes in the particular ballot box I registered my vote in. After checking carefully... he registered zero votes in all of the boxes in my section! I contacted him and he told me that several of his electors also experienced the same. Maybe Mr. Toffoli knows where the votes went.

I hope this answer makes exhaustively clear the array of events and facts that would be considered undeniably fraudulent in any modern democracy. Of course, in Banana Republics these are everyday (biannually, actually) occurrences.

On a positive note, the ongoing outcry against such illegitimacy resulted in enough pressure to pass a law requiring votes to be printed from 2018 onward, under heavy attack by the extreme-left. Also, with a high proportion of illiterate, naive and careless voters, the effectiveness of such laws in curbing actual fraud, remains to be seen.

This has not yet been established, and probably nevet will. The lawyer in charge of these questions is Dias Toffoli, long time PT lawyer who, to the suprise of most Brazilian lawyers, was appointed a Supreme Court judge by Dilma.

The press is not communicating enough about the issue of possible fraud in elections, even though many hackers have been critical. This is under communicated in the press, like most things.

Equally worrying is the fact that elections in Brazil is won by the party who has the most money. And that there are many indications that Dilma 2014 received money from the Petrobras kickback scheme. This is  (also) under communicated in the press, and the investigation of it in the TSE (organ that is responsible for investigating electoral fraud, remember Dias Toffoli) is gathering dust.