In order to get the audio driver to work for windows 8.1, I removed existing drivers, and ran the default Sigmatel driver in compatibility mode for Windows Vista. Detailed instructions below.
1. Disable default audio drivers. Open the device manager (Start > Search > "Device Manager"). Under "Audio Inputs and Outputs," right click each audio device and choose uninstall/disable
2. Download the default Sigmatel audio driver installer for the Inspiron 1420 from Dell at http://www.dell.com/support/home/us/en/04/product-support/product/inspiron-1420/drivers.
3. Set the downloaded file to run in compatibility mode for Windows Vista by right-clicking the file, and choosing Properties > Compatibility, checking the box labeled "Run this program in compatibility mode for", and selecting "Windows Vista".
4. Open the downloaded file and follow the on-screen prompts to install the driver, restart your computer as requested and you should be good to go!
Best of luck