As someone who regularly uses and hears this slang phrase, I can tell you that there are slight nuances in meaning depending on the context and tone. Generally the sense is that there's no help for a bad situation.

For example, expressing reluctant acceptance of an unfortunate situation, like: Pensaba ir al cine pero tengo que chambear, ni pedo (I was thinking of going to the movies but I have to work. Oh well). Disappointed tone of voice and often accompanied by a shrug.

Telling someone else to accept a similarly unfortunate situation: Ya sé tienes hueva de ir a chambear pero hay que pagar la renta, ni pedo. (I know you don't feel like going to work but you gotta pay the rent, so suck it up). Here the tone of voice is less disappointed and more like giving someone advice that they don't want to hear.

I could go on but I think you get the idea.

As for your examples:
"hasta los míos me han dejado abajo. pero ni pedo algún día saldré" My own people have given up on me, but no matter, one day I'll get ahead.

"pero me chingaron, ni pedo" But they screwed me over, nothing I can do about it.

Hope this helps.

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Note added at 3 hrs (2008-04-30 21:22:56 GMT)
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Sorry, in my 2nd example that was supposed to be "ya sé QUE tienes hueva..."