This pictorial is for the 2005-2006 Chevrolet Cobalt MANUAL TRANSMISSION. For the 2007-2010 Cobalt, this guide is the same for those vehicles. Only additional wire is the security light isolation. This can be found in your bypass module guide. Using a full featured bypass such as the iDataLink ADS-ALCA, Xpresskit DB-ALL2, Fortin Evo-All will minimize your wiring.
FOR MANUAL TRANSMISSION, YOU MUST TURN OFF DOOR TRIGGER MONITORING ON THE BYPASS MODULE, AND HARDWIRE
For automatic, no need to make any changes on the bypass module, besides having the correct flash.
Unit: Compustar 2W703SH-CN + FT7200 +
FT-DAS Mandatory for manual transmission when using the new 7x00 Compustar brains.
Bypass: iDataLink BLADE-AL
Firmware: BLADE-AL(DL)-GM2
iDataLink Bypass Guide
Vehicle Wiring Guide
Most connections are at the BCM. The brain was mounted above the gas pedal with plenty of room. Always bench prep to keep it neat.
Make sure you solder your diodes, as wrapping wire around solid metal is a poor connection. Diodes will create a "Y" where the 2 ends are the diode bands.
Above the OBD is a black harness. Look for a Yellow (+) wire, which is your clutch bypass. Connect your remote starter output to this wire. Get your ground from the ODB as well. Pin 4 is a direct connection to chassis ground.
After all connections are complete:
1) Program remotes to the unit (of not pre-programmed)
2) Close all doors, Open driver door to wake up bcm and proceed to bypass programming.
3) Program tach to the unit
4) Test system, pack it up and enjoy.
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Ted
2nd Year Tier 1 Medical School
Still installing as a hobby...pays for groceries
Compustar Expert
The cobalt/G5 platform is almost identical to my HHR which I did a write up here. 
https://www.the12volt.com/installbay/forum_posts.asp?tid=131309
This is obviously a manual transmission so it is slightly different.
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To master and control electricity is perfection. *evil laugh*