Apostolic succession in the West has components such as
1) physical laying on of hands
2) correct matter (i.e. a man over the age of X)
3) correct intention (consecrator wishes to make X a priest or bishop)
...this leads to the question that St. Augustine faced, "what if it happens by a schismatic bishop?" and the answer was that it is still valid if the three checkmarks above are followed. That means the followers of this bishop or even the bishop could be reconciled without repeating their sacraments.
Now in the East, different questions are asked:
1) Does the community of believers need a priest/bishop?
2) Does this candidate meet the needs of this particular community?
3) Is the bishop ordaining the candidate in communion with the other Orthodox bishops?
4) Is the consecration taking place in the context of the Eucharist of the community for which the candidate is being ordained?
5) (last) Is the candidate canonically eligible?
...So a bishop ordained by a schismatic bishop is *not* an Orthodox bishop, even if the book is followed, hands touch heads, etc. *IF* the bishop that is schismatic is received into the Orthodox Church, he *may* be received as a bishop *but* it is purely up to the decision of his brother bishops (example 1: Archbishop Lazar, a member of a breakaway Ukrainian group, was received by the OCA last year as a bishop; example 2: Two Old Calendar bishops in Astoria, NY were received by Patriarch Bartholemew who reconsecrated them bishops; example 3: A bishop of the Pangratios Church [don't ask!] was received by ROCOR as a priest only.)
Sorry for the longwindedness; I belive all this was necessary to set the stage.
Direct simony in the west, yes that was believed to "invalidate" an ordination. So some ordinations were ruled invalid. In the East, yes, that was sometimes the case. Some Russian Orthodox priests went into schism in the 1500's because of this.
Yet ordinations have to be seen organically and in the context of the above. God protects his people, so if a sinful bishop is ordained without their knowledge of the motive (ie money) and he is Orthodox and in communion with other Orthodox bishops, I'd say the Orthodox would probably still recognize his ministry although if they found out he would probably be deposed (but his ordinations, etc, would not be ruled "invalid").
As for the Turkish practice of selling the patriarchate: the candidates were already bishops, so in a way it's not the same thing--they weren't paying for ordination but rather for installation. Installation as patriarch is not a sacrament but rather an office in the Church, and actually an office in the Ottoman government. I like to look at it as more a payment from the candidate to the Turks to get a government job. Still very bad but not the same as paying a bishop to ordain you.
That being said, I think in our day we can thoroughly condemn the practice of the past and rejoice that it is not happening now (at least not on any widespread scale).
Sincerely in Christ,