How can you make your headphone and speaker jacks in your Dell inspiron computer play two different audio sources?

To your computer these jacks are both the same pair of channels. The only way you could accomplish this is to put one audio source on the left channel only & the other on right channel only, then adjust the balance on those jacks accordingly on windows volume control.

A better way to accomplish this may be to use an external USB sound card such as the creative extigy, note that your OS may or may not have the capability to utilize dual soundcards in this manner.