95 Chevy Lumina won't start

I have had trouble starting my 95 lumina for monthes. It takes me over 10 tries to get it started, especially on a cold day. If I turn it off and immediately turn it back on, it starts easily. Anyway, I just keep
it running like this for about half a year until today.
Here is what happened:
I started the car this morning to let it warm up before I drive it to work. After about 15 minutes when I came out ready to head for work, the car already shut itself down. Radio and all other lights on the dashboard were on though.
Then, I started it again, but it shut down itself again after about 5 seconds.
When I tried to started it one more time, you know what, everything is dead this time, all lights and radio except the dome light when I keep the door open.
I tried to jump it from my Camry with cable. It starts nicely with all the lights and radio on, but as soon as I pull the jump cable off, everything turns off again. Again, only the dome light on. I thought it would help to keep the lumina connected to the good battery on the Camry for a while just to charge the battery. Saddly, after 10 minitues of "charging" it still shuts everything down immediately after I pull off the jump cable.
you think I got a bad battery or what? Even worse now is I'll have to get it towed to replace battery or starter or alternater.
Thanks in advance for your help.
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Have the battery, alternator and ground/positive cables all checked.

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Alternator.
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-Mike-
snipped-for-privacy@alltel.net
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Put voltmeter across battery leads when running to see if you get approximately 14.2 volts on the meter. If it reads that, alternator is ok and battery needs to changed. if not charging alternator needs replacing.Good luck

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