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What matters is the evidence, which in this case is what are you doing with it.
a)Parked page: you can get into trouble for bad faith
b)Website : as long as the context/industry is different than that of the previous company, you should be fine.
But even if you do b) and if the previous company still owns the TM for the domain name, then they can still pursue it up with you, that is if they want to.
As others have said stay clear of anything that might confuse your activities with the old company AND don't do anything to capitalize on the domain's last intended purpose.
Still, to be safe, you should not try to profit off their reputation, or try to confuse people that you are somehow affiliated with them or else you are just asking for a nasty letter.