Turing died of cyanide poisoning, with an apple by his bedside, which was oddly and incompetently never tested but was somehow speculated to be laced with cyanide and consumed by him, supposedly inspired by a favourite scene from Snow White. He regularly ate an apple before bed and showed no intentions of suicide and made plans post death date. There's also no suggestion he was eating the apple because it was linked to being gay. I suspect being gay doesn't mean you have an increased biological desire to consume apples either. Also, Snow White was unknowingly GIVEN a poisoned apple, not created her own, which opens up a whole new line of conspiracy theories. However, another theory is accidental inhalation from cyanide fumes from apparatus in his room. Again, amazingly and incompetently not tested, so we'll never know.
Boring facts over, if you really want to find a very loose but potentially interesting co-incidental connection between Turing and Steve Jobs though, Turing died 24th June 1954. 37 weeks and 2 days later (around 9 months), Steve Jobs was born. Reincarnation, anyone?