I must say that the method you've described above is far from ideal. The best methods would be to buy a USB DI Box, or audio interface for your computer, and plug your guitar into that, or to use a microphone to mic up your guitar amp etc. Your question is about how to record with what you already have, though, so:-
What kind of guitar are you using; electro-acoustic, or electric? Just plugging a standard electric guitar straight into your computer probably isn't the best method. Without suitable (pre-)amplification, the audio signal your computer will be receiving from the guitar will be very weak. Chances are your computer is capturing it already with your current setup, but it's just too 'quiet' to hear properly.
Do you already have a guitar amp? If so, I'd suggest plugging your guitar into it, then use the cables and adapters you've bought to run between the amps headphone output to your computers Line-In (or Mic-In, if you don't Line-In).
I'm not sure you need a TRRS jack; as far as I'm aware this is just used by things like Apple devices, to allow for volume control of headphones etc. Please note though that the cable you've bought sounds like a standard stereo auxiliary cable, whereas the audio from your guitar/amp will be mono, so this may all end up with you receiving just a Left channel on a stereo input.