Let's say you can do a 3:30 marathon and have done a few HIM. What are the gaps in training to get to the top here?
One's sexual preference won't change the odds of summiting Everest.
Seriously though, I have no idea what a HIM is. Regardless, things one needs, in addition to money, time, and running long distances quickly include:
1. Ability to tolerate high altitude - as I said upthread, fitness doesn't automatically protect one from acute mountain sickness, nor other high elevation illnesses.
2. Physical strength, to lug a bunch of gear to the high mountain. Sherpas don't carry everything.
3. Mental toughness, to endure many bitter cold, miserable days-weeks.
4. Not being scared of heights, or precarious positions.
5. Mountaineering skills, including glacial traverse, self arrest, +/- rudimentary ice climbing.
And you need to be a little lucky, such that you don't get a cold or musculoskeletal injury, and the weather cooperates long enough for you to have a chance to summit.