2006 corolla- check engine light comes on. i replaced the battery (old) and i reconnect it, it runs fine for about a minute, no warning lights, then shuts off, check engine light is lit and will crank but not start. I disconnect the battery, reconnect it and same things happens again. All fuses are good,

There are multiple computers in the car that have to talk to one and other. There is the ECM or ECU and it talks to the BCM. Sounds like the BCM is having issues.

I do not believe the two are closely related but try disconnecting the battery and reconnecting it again. Only the negative side. also check for a loos connection.

It is possible that your battery is not charging at all, or the jump start has damaged the voltage regulator. Your battery should have been charged sufficiently after the 15 minute run, so there is another problem.
Check the voltage with a meter - I think Radio Shack should give me a bonus for recommending them so often, but you can get a relatively cheap (less than $5.00) meter from them that will give you an accurate reading.
Connect the meter across the battery terminals and check the voltage. It should be over 12v. With the engine running at just over idle the meter should slowly move to 13.8 or possibly as high as 14.2 volts. More than this, replace the regulator. Less than this, replace the regulator.
The regulator is mounted inside the alternator. It is usually possible to remove and replace the regulator without removing the alternator. The regulator is a fully replaceable unit complete with the slip ring brush gear, and is held in place by two small screws. The new unit should have a wire through the brushes holding them in place,
If it doesn't have one you will find the brushes are almost impossible to put back, so the trick is to locate the small hole in the front brush holder, then gently push the brusher into their respective holders - the brushes have tiny holes in them corresponding with the hole in the front brush holder. Now keep the brushes in place with a thin wire - a paper clip works fine. After replacing the unit, screw it down and then remove the paper clip,
Reconnect the little electric wire, and your problem should be fixed.

Sometimes it takes a few on/off cycles for things to reset.
You could unhook your battery for about a half hour then reconnect. This should help your computer forget the problem.

Does it run for a full minute or start then shut off within a few seconds?
If the latter, then it sounds like the anti-theft system has kicked in and needs to be reset.

Battery was diconnected for 1 minute and then reconnected. All lights are off.

dear friend-filling the tank has nothing to do with the engine light.in order to cancel this light,disconnect the battery and leave for a while.reconnect battery and check light,it should be of,if the same happen again take vehicle to a dealership for a diagnostic report.

beeps are warning signs. check: switch lights, seat belts, doors, engine hood, trunk.

It might leave you stranded. Because without the alternator. which I think is your problem your battery will run down in a very short time. Even if you had a new battery.Check the belt first as Toyota Ed suggested. If it's good, and not broken. Replace the alternator and if you have to, the battery also. One could affect the other.