Ford Explorer has lights and bells can be jumped but won't start after its shut off?

Yesterday the battery light came on whenever I took my foot off the gas and would go off when I gave it gas. Today I stopped ata store, when I came out it wouldn't start, jumped it, went the approx 2 miles home, shut it off, tried to restart it and NOTHING. WHat could be wrong. I did notice some white stuff on one of the battery thingies but 2 ppl said it is the alternator