What you need is a "line in" to the boombox, but I don't see this feature mentioned anywhere in the manual.
However, the speakers themselves are rated at a 6 Ohm load. You could purchase a small second hand stereo receiver to power these speakers and just be careful not to turn the volume control too high.
It isn't feasible for you to connect these speakers to the headphone output because:
1. Your computer does not have an amplifier powerful enough to make these speakers do anything. Even if you could connect the speakers (see #2 below) you would blow the output stage on your card, and need to buy a new card.
2.. The red wire moves the speaker's diaphragm out and the black wire moves the speaker's diaphragm in. Both left and right speakers have two wires each, and a stereo headphone connection only has two bands. You can't make the four wires match the two outputs.
So, should you purchase a small second hand stereo receiver, make certain that it has a "line in". You would then purchase a "mini stereo to 2 RCA" adapter to connect the computer to the receiver and the speakers then connect to the receiver for left and right sound.