Dead Alternator?

I was leaving work yesterday jumped in my jeep it started right up I drove for about five minutes shut it off went to start it up again no start it just barely cranked over no big deal I was on a hill so I bump started it but on the way home I could not get in to the throttle or it would cut out. so today I cleaned the battery terminals bump started it same thing it cuts out wnen you get it to the throttle. is it my alternator or what? it is an 87 with a 5 Spd any help would be great thanks.

Unlike cars of the past these NEED 12volts to run the fuel pump, if the alternator is bad the battery will drain pretty quick powering that pump so it would not suprise me if the alt was bad. Most parts stores will do a load test on them for free... or you can get one of those little testers that plug into the cig lighter and give you a voltage reading, should be about 14v running...

Also today while I had it running I pulled the positve battery cable and it just died so it makes me think it is the alternator.