Electret condenser microphones will deliver output even without plugin power. Really, really bad, low-gain high-noise output. So you better make sure that the plugin power is actually switched on. Depending on your audio hardware and your operating system, there may be utilities for controlling the plugin power, and of course the simplest way to be sure is to actually take a multimeter to a microphone jack (after connecting a naked plug or one end of a 3.5mm stereo audio cable).
If your microphone input is mono, some sockets are actually stereo sockets wired with plugin-power only on the ring. Connecting this with a bona-fide mono connector will just short-circuit the plugin-power (in order not to hurt microphones that don't want plugin-power): you need an actual stereo plug/adapter then that takes tip+ring to the microphone.
Many audio chips need some command to switch on plugin power: then you might need to fire up a suitable utility.
In short: there are various ways in which plugin-power might not make it to the microphone. Make sure that it does before checking out other options.