I have a astro start remote starter (series 120A) on my camry 98. I am only able to lock the car using the remote. Car doesn't start and there is no parking light indication as well. I am also not able to unlock the car using the remote. Is it a programming issue or starter brain is gone?

SOURCE: Toyota Camry 2008 Locked by Security System

The computer for the alarm is probably causing your problem. Scan the anti theft module to trouble shoot for the problem. You might have a door sensor that is shorted.

SOURCE: 2005 Toyota Camry - Electrical Issue

Let me ask you this:
Is there ANYTHING on the car that is not "factory"? (remote starter, burglar alarm, aftermarket keyless entry, etc)

If your answer is "yes" to any of the above, you may have a damaged body control module (BCM). Any Toyota with a BCM can experience a BCM failure with certain remote starters, etc....
If so, it is rather expensive to replace.

SOURCE: 2000 chevy astro starter problems

replace the starter

SOURCE: central locking remote won't open car/car won't start

Sounds like a basic bad battery. Even though its not that old it can be bad....and probably under warranty. Immobilizer or starter will not cause that. Get the bat tested.
Only other thing is called a "parasitic draw". This is when something is drawing current from the battery when its supposed to be off. Usually this causes a totally dead battery, not a weak one like you have.

SOURCE: I can't disconnect my '98 toyota camry car alarm.

BEHIND THE DRIVERS KNEE PANEL IF IT IS FACTORY IT SHOULD BE JUST BEHIND THE DUCT WORK YOU CAN ALSO JUST UNPLUG THE PIGTAIL HARNESS IN BETWEEN THE IGN. SWITCH AND THE ALARM (PLEASE RATE THIS)