Evet though its a bit dated it still can give you a clue on what the error codes mean: CNET - How to invoke and interpret the Apple hardware tests.
So if we dissect your error: 4sns/1/c0000008:TC0p--124
- 4SNS System sensor
- T for temperature
- C Central processor (CPU)
So we now have a diagnostic direction something in the CPU cooling is not working correctly. And you do here the fan going at full speed so the system is trying to lower the temp but unable to. So either the CPU fan or the heat sink is not working correctly here.
Lets try something that can give us a bit more here. Download this app: Temperature Gauge Pro. It should show you in more detail what the sensors & fans are upto. Post a screenshot for us to see in your question (go into edit mode or append an update to you question).
You're at a crossroads here.
You may want to let Apple fix this as it could be a bad circuit on the logic board or the heat sink has a problem. If you decide to do this your self the newer 'Thin Series' iMacs are very different than the older models and you do need to be very careful in removing the display unit as you can easily damage it in the process.
Make sure you have the correct tools as outlined in the IFIXIT guide here: iMac Intel 21.5" EMC 2544 Display Replacement as well as this tool: iMac Opening Tool. You will need a new set or two of the adhesive strips as well.
At this point you'll need to open the system up and do an inspection of the fans cable is not damaged as it has the tach sensor within it. Are you up to it?
Follow this IFIXIT guide: iMac Intel 21.5" EMC 2544 Fan Replacement Jump to step 24 to compare with your fan cable connection.
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