My cars stalls after 10 min and won't restart until I wait 30 min.

My battery light came on the
other day so I hurried home but
before I got home the light went
off.  This morning the car started
and idled for 10 min. And stalled
and when I tried to restart it, it
acted like the battery was dead,
just a few clicks, or just nothing.  
In 30 minutes I went to start it
and it started right up only to
stall out again and again
wouldn't restart for 30 min.  I
cleaned the battery terminals
checked alternator belt, reset the
security system, and I just can't
figure it out and I'm not in the
position to be able to buy
expensive parts for trial and
error.  I am getting a new battery
tomorrow because mine looked
awful with corrosion and I have
no way of knowing how old the
battery is.  Plz if anyone knows
what could be up with this P O S
could you plz keep your reply
simple.  I'm no motor head by no
means but I've started doing
what I can on my own vehicle
(so far brakes and rotors, oil
changes, some sensor changes
etc.)  Thank u all -- Nicole