2004 MAZDA MX 5 1.8 petrol Do not Start

Hi I am having problem starting my Mazda 2004 mx5 1.8 petrol, At first car had a dead battery (i.e no spark at all) tried to charge but battery did not hold the charge even in this stage car was starting and running alright if start with jump pack once I started the car and press the emergency hazards light's button on dash suddenly car cuts off and engine stop running, then I change battery.... No problem start fine after that one morning I put key in a ignition it refused to start only starter motor was trying to turn the engine but was fail to start it, I thought it may not have enough petrol in it so refill With one green petrol cane... turn key ON... sorry no luck.... checked the Dip stick it was showing no sign of engine oil then Following steps taken.

Change Engine Oil Spark plugs Oil filter Air filter,
Clear all Air and petrol hose with High pressure compress Air
Checked All fuses either in Engine bay or under the Dash No problem found

tRY TO Start the car again but No luck

Attached OBDII to check if there is any fault may have been reported by the ECU, Even there is no Engine Management light was ON I tested any way.... following screen shot was displayed by OBD11

https://www.facebook.com/photo.php?f...type=1&theater

Just to inform you that couple of times ignition key turned ON and keys was left in key whole, there was a car and Key sign flashed on the dash board display unit

could any one tell me what that might be...

Is it immobilizer or there is some sort of economical function which may have kicked in when car keys was left in the key whole which is not allowing car to start or any thing else, Note I don't have user manual or remote control for central locking for this car..

Can someone plz help me starting this car

Thanks