Hmm.
A mis-matched impedance could be the cause of your problems but I've been plugging microphones into amplifiers, etc for years and my experience is that you can usually get away with using most microphones with most circuits (irrespective of what you should 'theoretically' use).
See if you can borrow a microphone with a higher impedance from a friend. (Alternatively, keep an eye open in 'pound shops', and the like for a cheap microphone which states that it's got an impedance measured in thousands of ohms, rather than hundreds. It might not be good enough for quality recording but, if it only costs a pound or two, it will reveal whether the problem is related to mis-matched impedance before you invest 'proper money' in a better mike).
Chris