My onboard sound is crap

So I've been using my logitech G35's for well over 4 years now, but now I want to step up my audio game and so I'm getting Audio Technica ATH-M50's next month. 

In the meantime, I bought a cheap desk microphone on recommendation from a friend of mine.
The problem I'm having with these is that the volume of the microphone is very low.(I am using a desktop by the way)
Increasing the gain DOES help a lot with the volume, but well, it also adds a lot of static noise which is annoying for the people listening to me.

So I plugged the microphone into my laptop and it worked fine. Volume was fine and no static noise. 

I have a MSI 870A-G54 motherboard which has a Realtek® ALC892 audio chip.
I have tried updating the drivers but it had no effect.

Would buying a dedicated soundcard(a cheap one, like the Asus Xonar DG) eliminate these problems?  
Or would I be wise to save some money and get a DAC when I'm able to? 

I live in the netherlands so I'm not quite sure where and what DAC to get since the options are a bit more limited here compared to the states.

Any input would be appreciated

Is the problem mic connected to your computer with a 3.5mm jack or by USB? 

By 3.5mm jack