I will be using a boombox connected to my computer (headphone jack from boombox to headphone jack in my laptop).
Nope! 
Sound comes out of the boombox headphone jack and out of the computer’s headphone jack.
I had done this years ago with ease
You probably had a desktop/tower computer with a regular soundcard with line-inputs. (Almost all laptops only have mono microphone-in and headphone-out.)
If you have access to a desktop/tower computer, the line-input on the soundcard is a good match for a headphone-level signal (or a line-level audio signal, of course).
Otherwise you’ll need a USB audio interface with line-inputs. There are a couple of recommendations on [u]this page[/u]. Different interfaces will have different input connectors so make sure you have the correct cables/adapters.
If anyone can provide STEP BY STEP instructions for this, I would appreciate it. (Please do NOT assume that I know anything about audacity or recording).
Let’s just start with getting the equipment connected and recording. Once you have a connection you can select the hardware & connection as your [u]Recording Device[/u] and click the Record button.
If you have trouble recording, or with the steps following recording, let us know.
After recording you can save your Audacity project and/or export to WAV (before editing). I generally recommend you export to WAV whether you make an Audacity project or not.
CDs use the same underlying format as 16-bit, 44.1kHz, Stereo, WAV files. Audacity doesn’t burn CDs so you’ll need different software for that. Depending on the hardware and how you do it, you can make separate WAV files for each song or you can make one big WAV file with a cue sheet to place the track markers.
To export as MP3, you’ll need the optional LAME MP3 encoder. As you may know, MP3 is lossy compression so do all of your editing in WAV or as an Audaciy project, then compress ONCE as the last step.