your laptop probably has a mic / speaker jack. There should be a little painting of both near the jack. Your PC only has a speaker jack (the green one). If you hook it up to the pink one you will be able to use the microphone but not the speakers. You'd need this
You didn't mention how it's connected to your laptop, but some headphones (including yours, judging by the Amazon page) can run the mic and headset through the same cable.
Your sound card may not be able to pick up that it's a 'dual-cord', however. My PC has this problem. You may need to be split the cord manually to the headphone and mic jacks.
http://www.amazon.com/Smartphone-Headset-Adapter-Audio-Female/dp/B00SY8V4G4
Something like this may be what you're looking for. Hope it helps.
You got the wrong kind of splitter. The one you got just combines two sources into a single stereo jack. You need something that splits the microphone from the audio, like this: http://www.amazon.com/dp/B00SY8V4G4