Battery died, sat, replaced, runs on plain key. Told to drive to reset so will smog. How far?

Disconnecting the battery resets the PCM - engine computer ,an the emission monitors . A drive cycle has to be done to get the monitors to run an hopefully set. That's all you need to do is drive it for few days of different driving conditions - city , highway ,from cold start . google GM drive cycle . OBD Monitor Not Ready

Clean out your egr valve.

Most likely the alternator is bad. Best way for you to check is start it up, then pull the negative cable off the battery. If it dies the alternator is dead. As far as it draining when parked, I have replace a lot of the ignition lock set and keys because you can put it in the accessory position(All the way back) and pull the key out. Leaving on things like the radio.

LSI 4cylinder or 3cylinder? engine. , all answer USA cars.
all answers now, are 3cylinder

did the odometer quiet too?
key fact
and in USA< connect any scan tool and see if VSS died.

the usa 96, 1.0L 3cyl has the VSS sensor in the speedo
and when the cable snaps, Speedo to transaxle flex drive cable.
snamps
the speed goes dead
the odometer goes dead
and Vss goes dead.
easy huh, if all 3 are dead.
but if speedo ONLY goes dead, that means ITS dead.
vss= veh.speed sensor. or MPH sensor.

150 miles at least also check ur air filter change nice clean one

The vehicle owner does not do drive
cycles,a repair shop should do that

Do you even know what the drive cycle
requirement was?

Have you not considered a repair shop
& some testing, to find out about the dead
battery & check engine light issue?

You don't go to inspection when you know
you have problems, nor until you look at scan
tool data, to see that all the monitors have run
& are clear,just waste your time at inspection

The system has to see a wide range of conditions before a smog test can be done. On most brands you have to drive at least 50 miles, at various speeds including stop and go, let it idle for 5 - 10 minutes, and run at freeway speed for at least 25 miles. It also has to reach normal operating temp of 195 degrees.

Here is the procedure for allowing system to run each of the separate mode tests.
EGR : Start engine and warm up completely. Make sure all electrical loads are off (A/C headlights, blower fan, and rear window defroster) Accelerate to between 49-57 mph and hold a very steady speed for 1 minute. Decelerate to a stop and turn off engine.
EVAP : Ensure Baro pressure is 21.3 inHg or higher, Intake air temp is 41-95 'F, Fuel tank level is between 25-75%, Battery voltage is 10.9-14.6 volts. Start engine and idle for more than 10 seconds then turn key to off. Leave vehicle to sit for 5 hours or more. Start engine and race to 3500 rpm to warm up completely the idle for more than 15 minutes. Accelerate and then drive vehicle at very steady speed between 40-50 mph for more than 5 minutes. Stop vehicle and turn key to off. Leave vehicle undisturbed for 20 minutes or more.
When I say steady speed in the above, try to keep dead on to a set speed to help ensure the test is run. Especially for the EGR as this is when the test will be performed and if speed/rpm is not very steady then test will not be performed. The Evap test will be ran during that final 20 minute or more sitting period (or should be anyway).

Some monitors in the computer may need 500 miles of different driving styles and speeds before they are happy and many "start from cold" driving cycles.
DON'T RESET anything and DO NOT let the battery go dead or you will have to start over.

This means you must drive the car long enough for all of the self-tests to run. Depending on the test it could be a single start and run to many cycles and many miles. Usually after about 50 miles of driving you have completed most tests.
I'm not sure where you are located, but in Ohio you can ask and have the car run on the dynamometer and compete your smog test this way.