GSM Modem will not register to network
Solution is to reflash SIM900A with SIM900 software and it works like a charm.

Here is the page that shows the solution.


  Flashing is no trickery, just a right sequence of operations, there is
  detailed instruction for arduino-like approach, my way required just a
  few major steps:
  
  
  Power up your SIM900A module to respond to AT commands in auto-baud
  mode (AT+IPR=0). It means you must wire powerlines, do power-on
  sequence with PWRKEY etc.
  Setup flashing tool — connect it to SIM900A, set default speed of
  460800 baud, choose firmware to flash from unpacked RAR file, select
  “don’t check file name” check-box and press “start download” button
  to see “Power On/Reset Target” message.
  Short NRESET (pin 16) to GND for a moment. Right after it reboots
  flashing tool will start pushing data.
  When flashing ends with “Download complete” power off SIM900A
  module. Note that reset will not work, disconnect power line and
  start power-on sequence once again.
  Voila! It works now as expected. PIN accepted, logged in to network
  and test text message successfully sent to my smartphone.
  


Thanks everyone for helping out!