If you are using the original coded key with the security sensor in it your battery may need replacing (in the key), now if you are using a copy of the coded key ...bad news it won't work because it doesn't have the code programed into it.
Sounds like it is not charging, have the charging system tested, it may be the alternator at fault.
It sounds like your alternator is no longer recharging your battery. You probably need a new alternator.
There is most likely something in the gas tank. When the car starts the fuel pump starts sucking in fuel and when the trash gets to it the gas will not be able to flow through the clogged pump so the car stalls. When it stalls the fuel pump stops suction and the trash comes out allowing it to start again.
my 98 does the same but not with a/c on. I have only found fuel filter/pump suggestion as with 96 blazer stalling while driving. Will check out and let you know.
my suburban wont start
car starts but shut off while driving
the idle jet in the carb is blocked and needs to be cleaned out and reset
Possibly Crankshaft Position sensor
Buick Blazer
'Blazer'.
Such numbers were issued in Connecticut.
Idle Air Control Valve.