Gently pull it out, dispose of any debris, and repeat as necessary. Insert the tape end into the headphone jack and twist it a couple times. Make one linking to the TVs audio output, plug the speaker system into the wall. Wrap some tape around one end, being careful to not wrap so much that it's larger than the headphone jack. But for under, you can easily add an AUX input to your Series 1 all by.
Move it around gently and try to pull out the lint. Then insert that end into the headphone jack. Put a tiny bit of rubbing alcohol on the end you removed the cotton from. Remove most of the cotton from one end of the swab. Right click on the Speaker Icon on the taskbar, click Playback Devices then I select Speakers and click Set Default. This may be enough to remove anything that's built up in the jack. You may need to shine a light into the jack to get a good look.