According to my repair information the:
11- Transmission code present
53- Knock Sensor Circuit
83- Low Coolant
27- Quad Driver Module Failure
The 27 could be the code that is setting the 11 trans code present. The driver module is integrated into the pcm. This controls some of the outputs an could be the one for the transmission output. The 53 is for the knock sensor which may have picked up noise from the coolant being low. This may cause you engine to make noises such as knock, ticks etc. The knock sensors job is to let the computer know when the the engine may be running lean from the pinging in the engine. Is the coolant low? From the code 27 it sounds like the pcm will need replaced. Saturn has not released alot of information on this code or a diagnostic stratagy for it. I would chewck the coolant level to see if it is full if not find the leak and have it fixed. I would then reset the codes and see if any come back. If any come back right away then you have a hard fault code. This means the problem is happening all of the time. If they do not come back you should be ok.
From the codes you posted and the repair information I have I don't see any problem with the transmission. I cannot say for sure since I am not there to road test the vehicle to see if it is shifting correctly or if it has any other noticable problems. The PCM is the powertrain control module or the engine computer. It just depends on who you talk to will call it different things. Either way it is the engine and transmission controller. I also am not saying that there is not a problem with your ignition switch , but the codes above indicate nothing about an ignition switch. There isnt even a code for ignition switches.
Automatic transmission you are looking at around $425 for a pcm from the Saturn dealer. You may be able to find one aftermarket or possibly used. Labor time is about 1/2 hr. This will either need to be done at a Saturn Dealer or a garage that has access to the Tech II scan equipment by GM. The new module will need to be programmed to the vehicle in order for it to run.