There is probably a difference in the jacks on your PC and Laptop.
The mic jack on your laptop is probably an actual mic level input.
The jack on your PC is probably a line in/mic in combo jack, which is a line level input.
There is a big difference in the signal level expected from a mic input vs a line input. Microphone's produce a much lower signal level than line sources, which is why microphone's typically go through a pre-amp before hitting a line level input.
I am going to assume you just have onboard sound on your motherboard, which means you will need to go in to your Realtek (most likely) sound panel and turn on the 'mic boost' for that jack to bring the input up to line-level. Your windows 'recording volume' for the microphone should be 0dB (right click the 'volume' slider and you can change it to decibels). The windows mic boost, if it's there, should be off.
So to summarize:
Set windows recording tab volume for the mic to 'decibels' instead of 'percent'. Set to 0dB. Turn off mic boost in windows recording tab if present.
Go into Realtek Sound Panel. Find and enable mic boost for the line in jack and set the recording 'volume' (it's actually gain, not volume) to max. Test in discord and report back.