Using audio output if the device is not detected under windows?

Question

Windows

I have an Asus UX32ln laptop. The 3.5mm jack on the laptop is broken so that it does not see the connected headphones, but the headphone port itself works: under ubuntu you can make it stream sound at 3.5mm, while there is sound in the headphones, without distortion.
It’s problematic to get a 3.5mm port in Russia, I’m dealing with this issue, but I want some kind of intermediate solution for Windows.
Technical information:
Intel Lynx Point-LP - High Definition Audio Controller [B2]
PCI\VEN_8086&DEV_9C20&SUBSYS_15DD1043&REV_04
Conexant 8.66.16.52 The software solution is of
interest.

Answer 1

I want some intermediate solution

USB headphones or headset
X3

Answer 2

The 3.5mm jack on the laptop is broken so that it does not see the connected headphones, but the headphone port itself works

even not quite clear how it is?