The way you get around the security system on the Cobalt is to reprogram the PCM. You will need a Tech II scanner or a scanner that can program GM modules. Otherwise there is no way to get around the security system in stock form unless using a stand alone PCM to control the engine and transmission. The security system is integrated into the PCM. The same goes for BCM and TCM. They all have to work together and would have to have custom programming to make changes. If you have an older model, 05-06 with 2.2 engine, which you do, you are shit out of luck. The PCM is deemed non-modifyable. Might be able to try the dealership, maybe. They may still be willing to do the changes, but it’s getting hard to get them to do anything on the older GMs when I’ve inquired. Since you’ve got the 2.2 early year, it’ll use a 16 bit PCM, later ones use a 32 bit and are easier to modify. The 2.4 engines used 32 bit PCMs through all years and are able to be modded.
Maybe someone here knows how to rig the car. But I have a feeling it’s a no go because of the anti theft device in the lock cylinder and pick up unit that goes around it. You can actually find a locksmith to make a key, and reprogram it though. This is probably the best option compared to rigged it or reprogramming the PCM. Personally, I would just spend the money and get it done right. It doesn’t cost that much to get the key made and programmed. In fact I need to make keys for my Cobalt soon since I just have the one key. I also got my car on the cheap. Paid $300 for something I was able to immediately able to daily drive that just needed some maintenance. I will probably go Saturday to get some key as I had some bad luck last week with the key. First I left it in a friends car that lives out of town. Got the key back. But accidentally locked the key in the car. Luckily these cars are easy to break into if you have a slim jim tool. Very easy to get in.