Microphone not working

Hi all.
I have a situation, I dont undestand.
I use an Ultravoice XM8500 Dynamic Cardioid Vocal Microphone.
This has been working perfectly fine on my “old” laptop, and stationary PC, using the standard Microphone mini jack connection.
I have however gotten a new laptob, that only have a “combo” headset / microphone jack connection. I have therefore bought a “splitter” cable.
Now I am unable to use the Ultravoice XM8500, no input is registred on the microphone, when connected.
However the connection is working, because if I connect a normal PC microphone, all is ok.
I just dont understand, what the difference is, of the “standalone” microfone inpuds and the Combo, and why not working using the combo with a splitter cable.
Is there any way of a workaround. The new Laptop a HP Pavilion only has the combo possibility of connecting a microphone.
kind regards.

What does this splitter cable look like? The ends of both specifically. Do you have a link or a photo you can share?