are you using the front or rear jack? in many cases the rear jack is not amplified heavily (for use with speakers, so it matches the rest of the outputs there) while the front panel jack is amplified more for use with headphones. use the front jack if its a tower pc.
the iphone like most apple devices tend to have decent amplifiers in them. the m30x, m40x and m50x are easy to drive as well so work on most devices. i have a m50x myself and it works on practically anything. even most lower end onboard should drive it except in some cases where the onboard amplifier is really bad.
if your motherboard states compatability with 300ohm headphones (keep in mind.. just listing the impedance is not a true way to gauge such things) then it likely has at least a fair amplifier so should work with easy to drive cans like the m40x. this points to perhaps you not having drivers for your onboard audio (i've seen this happen in the past) or using the wrong jack to connect your headphones.
the first thing i would do is uninstall your audio drivers and reinstall the newest one found on the manufacturers website. restart. plug the headphones into the front audio jack. any change?
i'm hesitant to say its because your computer has a weak amplifier but it very well may be true despite any claims they have made. it wouldnt be the first time i've seen grossly inflated stats to try and make a sale. even a lowly xonar dg can quite easily power the m40x so that is certainly an option as well.
another thing to look at is not just the windows volume level, but the volume level for applications and games or videos. the two work together. generally for things like videos i max out the bar and just adjust windows volume (well.. on my main system i have a knob on my receiver i use, but same concept..)