My 1996 corolla has DEI alarm w/ remote! lately when I lock car w/ remote and then come back and unlock w remote the car wont start up at all there is nothing when I try to start car and turn the ignition key,like dead battery but battery is good in car and remote battery is new and good also,so i disconnect car battery and hook back up sometimes I do it several times and it then may start up, but this is happening every few days

This is most likely caused by the car's anti-theft system. Most newer cards require a separate module to be installed to override the anti-theft system while the remote start is in use. Otherwise, when the anti-theft system detects an anomaly, it will immobilize the vehicle.
DEI makes a 556H module for this purpose. The link shows the instrall manual for this device.

DEI 556H Module Info

If you have a push button key or remote try locking it then unlocking it. If that isn't applicable try using the key on all the locks on the outside of the car, do the same, lock then unlock all the locks including the trunk. How long did you leave the cables off the battery. And did you pull both cables off or just one? Security systems sometimes had circuits that ground out separately and had large capacitors capable of sustaining power along with the Safety Restraint System for a matter of minutes. Sometimes computers won't reset until after 20-30 minutes with no power.
I am also assuming your issue is that the alarm is gong off and that you are not having a security light on the dash, with a no start issue, or an issue with the security code for the radio.

2nd-ing the 'unlock door with key' trick

Try to close doors and lock it with the key , not remote.
Then take the key out , wait 20-30 sec. and unlock it with the key.
After that try to start engine.

If unlocking the Van via the door locks wont disarm the alarm it's because the alarm harness have become detached. The door panel will have to be removed and the harness manipilated manually to disarm the alarm. Or you can have a new remote programed

With alarm activated your ignition is disabled.Find the combination to disable it.With GM's you hold opposing buttons on the fob till it beeps twice. The dealer should help for no charge.

Check your remote to see that it isn't setting off the alarm. If the battery is dying on the remote, this could happen. If not, have alarm checked.

The alarm might have a relay to kill the ignition. Disconnect the negative or ground from the battery, wait five minutes then connect it again. This is to try and restart the alarm. Then lock and unlock the car to get the remote in sync. Try and operate your vehicle now and let me know.

I had the same problem, i had to remove the whole alarm system to get my car to start, when you unattatch the battery cables, the alarm notices the battery drain and sets the alarm off, i have no idea how much the dealership would charge for a new remote, but im sure its pricey, i would recommend just removing the alarm system, temporarily, until you can get a new remote. Good luck and god bless

try unhooking battery cable. hook back up and use key remote to unlock car and try to start if no remote use key to unlock